Q: Broke iPhone 5, now using 3GS

What "code" are you referring to?

It may depend on the version of iOS on the 3GS - can you say what is iOS installed on it? Settings > General > About should state that.

I'm not sure that you need to register a device to use it, can you clarify what you are you trying to do? You may be able to login to Apple.com to register a device…

https://supportprofile.apple.com

I think 2 factor/ 2 step authentication is managed via your Apple ID account settings.

https://appleid.apple.com/

I recollect using 2 step authentication with a 3GS, so it should still be possible.

I'm not sure you want to do that, however it will probably solve your current problem

There are limitations on changing 2 factor & 2 step authentication (like 30 day account change locks), look before you leap…

Frequently asked questions about two-step verification for Apple ID - Apple Support

iOS 6 should support it, however I can't see any actual info from Apple that states that as a fact, sorry.