In a file directory, how can I only get the file-name which contains a pattern inside the file using awk?

for example, there are 3 text files in a directory,

file_1, file_2, file_3

I'd like to find the file (I need file name only, not the line contains the pattern) which the file body contains a word "testing". How can I do it using awk?

Thanks

ls -1 | awk '/testing{1,}/'

why awk?

the purppose I want is find the file which contains a pattern in the file, not in the file name

grep -l testing *

In this particular case, the line in the file is too long to over the "grep" command's limitation, so neither "grep" or "egrep" or "fgrep" won't work. That's why I need find out how to do it either "awk" or "sed"

Best