find / -mtime -1 should do the job. You could direct the results into a file with: find / -mtime -l > files.txt
However, its unlikely that all of the changed files in an exploit will be found so easily. You face having find out how you were hacked (so it won't happen again), scrubbing your machine and re-installing. Hope you have clean backups of your data (if any).
Ouch. Once the server has been hacked, every file on it becomes suspect. If they planted one file in your system, you can expect that there are many more and that your system files have been replaced with bad-guy files that contain stuff like hidden backdoors, keyloggers, detection scripts, etc.etc. Most likely your log files have been altered, as well.
The only sure way to recover from a hack as you describe is to wipe the machine and reinstall the OS, then reinstall your user files from a known-clean backup, from prior to the break-in.
Once you do the OS reinstall, be sure to (a) "harden" the system with a tool like Bastille or similar, (b) install a few IDS (Intrusion Detection System) programs to continually monitor your system for attack attempts and (c) instigate a full backup procedure that dumps the data to a secondary drive that is not normally accessible (i.e. mount it, do the backup, unmount it).