On my system, the www-data user does not have write permission to its own home directory (/var/www). For --gen-random (but not for --enarmor), GnuPG wants to create a ~/.gnupg directory and fails, which it considers fatal. This works:

gpg --homedir /tmp --gen-random 1 16

...although it creates two files in /tmp and emits messages to that effect. Note also that it does not work if the two options are reversed—the --homedir option has to be first.

I don't know if that's your problem or not, but it's worth checking. (As already suggested, check your error log.)