Anyone can make a cheat code.
It's pretty possible in the world of cheating to basically alter your game in any way possible! From what I find over the internet, there are no cheat codes available to catch a Mewtwo in Cerulean Cave. However if you want you can go onto some other forums and ask for a cheat code if you want, for example getting rid of that guy blocking the Cerulean Cave so you can happily waltz into the cave. :P
I have no experience in cheating, so I can't really help you there, but some people know a lot more than me. xD
Hope I helped. :)