How to do full-text search and return coding for a new column?

This code will do it. (NOTE: The code using List.Generate is cleaner which is a but further down in this thread.)

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("RY07DgIxDESvMkq9ewbEp6GjQKKIUpiNIZZYg5LsIm5PYgq68fP42Xt3oFUipCBxZhcG786i1MGD20rvxo6gGSeunG20NMCapBF7qqDMf8elpy7ZPa8bI1tVqzZg1fmDWxbWWH7G9q0wJqpTGpcX3lIT2o0L4Qs=", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [#"Full-text search" = _t]),
    #"Simple Replace" =
        Table.AddColumn(
            Source,
            "New Col",
            each
            try
                Text.RemoveRange(
                        List.Accumulate(
                            {0..Table.RowCount(Text)-1},
                            [#"Full-text search"],
                            (state, current) => 
                                let
                                    varCurrentName = Text[Name]{current},
                                    varCurrentNumber = ", " & Text[Code]{current} 
                                in
                                if Text.Contains(state, varCurrentName) = true
                                    then Text.Combine({state & varCurrentNumber})
                                    else state
                        ),
                        0,
                        Text.Length([#"Full-text search"]) + 2
                )
            otherwise ""
        )
in
    #"Simple Replace"

For it to work, you need a query called "Text" that is the following code:

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WcspPUtJRMlSK1YlWcszLA7KNwGznxBIg2xjMDkgtSS0C8kzAPN/EokogxxTMCcnMSwRyzJRiYwE=", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [Name = _t, Code = _t])
in
    Source

The Text query looks like this:

THe main query - the big block of code at the top, starts with just the first column, and ends with the 2nd column being added:

See below to put that code in your Query editor to play with.

1) In Power Query, select New Source, then Blank Query
2) On the Home ribbon, select "Advanced Editor" button
3) Remove everything you see, then paste the M code I've given you in that box.
4) Press Done
5) See this article if you need help using this M code in your model.

I was able to do it with a 'Merge as New' on the 2 tables.

Select Name and Full Text Search column and use Fuzzy Match to perform the join.

Options (Threshold 0.5 and Ignore case)-> Others may work, these were just the second ones i tried

I think there's probably a solution without the merge and maybe using Text.Contains function.  If I get time tomorrow, I might try it. 

You could perform the task with the following steps.

Define a record having names as fields and codes as values.

Split text to list of words and transform that list appliing the function record.fjeldOrDefault. wrap that in the function list remove nulls and then combine the elements of list tighter with ";".

https://community.powerbi.com/t5/Power-Query/Replace-multiple-values-in-multiple-columns-in-one-step/m-p/1222106#M39526

Anonymous - Got it in a cleaner step.

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("RY07DgIxDESvMkq9ewbEp6GjQKKIUpiNIZZYg5LsIm5PYgq68fP42Xt3oFUipCBxZhcG786i1MGD20rvxo6gGSeunG20NMCapBF7qqDMf8elpy7ZPa8bI1tVqzZg1fmDWxbWWH7G9q0wJqpTGpcX3lIT2o0L4Qs=", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [#"Full-text search" = _t]),
    #"List Generate" = 
        Table.AddColumn(
            Source,
            "Generate",
            each 
                let
                    varTotalRecords = Table.RowCount(Text),
                    varCurrentText = [#"Full-text search"]
                in
            Text.Combine(
                List.Transform(
                    List.Generate(
                        () => [x = -1, y = {}],
                        each [x] < varTotalRecords,
                        each [
                                y = 
                                    if Text.Contains(varCurrentText, Text[Name]{x})
                                    then [y] & {Text[Code]{x}}
                                    else [y],
                                x = [x] + 1
                            ]
                        ){varTotalRecords}[y],
                    Text.From),
                    ","
                )
            )
in
    #"List Generate"

It uses List.Generate to cycle through each record and build a list of the hit codes. The table returned is:

My full PBIX file is here with both List Accumulate and List Generate.

Anonymous - can you advise if any of the above solutions work for your needs and mark it (them) as a solution? 
If none do, please reply back with clarifications so we can assist.