For example, if I force a container to stop with kill, then docker-compose ps to check my containers, I get State as Exit 137. And with docker-compose stop I get Exit 1/Exit 0
As there are no documentation for exit code, can anyone please explain to me the meaning of it?
This has not so much to do with docker as with the system it is running on. If you take a look in this table of reserved exit codes for bash, you can see the line:
128+n Fatal error signal "n" kill -9 $PPID of script $? returns 137 (128 + 9)
Which corresponds to the 137 you mention. It is 128 + 9 (SIGKILL), which you can see in the signal(7) man page. Normally a 0 means a clean exit and 1 there was something wrong, these two can suffice for a programmer. They can however range from 1-255, including the reserved ones mentioned above.
This is just a short answer as I am not an expert on the subject, you can find more on this unix.stackexchange thread on default exit code when process is terminated or perhaps someone here can give a much more elaborate answer than mine.