Full text search on larger text rows

I am wondering what is the best practice to use the right query in my case.

The problem is I tried the LIKE and ILIKE and it was faster then pg_trgm and the postgres full text search, because they often run in a timeout or throw an error:

NOTICE:  word is too long to be indexed
DETAIL:  Words longer than 2047 characters are ignored.

So I am not sure, if I did it right and my table looks like this and has over 10.000 entries:

  Column   |     Type      | Modifiers
-----------+---------------+-----------
 id        | integer       | not null
 doc       | bytea         | not null
 textdoc   | text          | not null

So I have the document (PDF or DOCX) and I give it to the converter which makes a huge string out of the documents and put it into the textdoc. A document can have 150 pages or 40.000 words(strings). So in each textdoc can be a huge amount of words. And when I have over 10.000 entries in the database and each of this entry has a huge amount of words in textdoc, how can I speed this up.

So my actual query looks (simplified) like this:

SELECT * FROM mytable WHERE textdoc ILIKE '%word from input mask%' 

When I am searching the web, the standard message is don’t use ILIKE. I used pg_trgmand it wasn’t really faster. It was all about three minutes for a query.

Required information:

Database: "PostgreSQL 10.4 on x86_64-pc-linux-gnu, (Red Hat), 64-bit"

Analyze (hope I did it right).. I run:

EXPLAIN (ANALYZE, BUFFERS) SELECT * FROM mytable WHERE textdoc ILIKE '%word from input mask%'

Here is the output: https://explain.depesz.com/s/wqLh

Another question is, the notice of the 2047 characters: Does this mean, that a the text in the column textdoc is over 2047 or a string in the textdoc is over 2047 characters?

select alias, description, token from mytable cross join ts_debug('english',textdoc) 
    where length(token)>2047;