I'm technically an aerospace engineer, but all I do is code most days. I think it depends highly on what you do, since my job also involves doing things not strictly coding related as well, I always slap the engineer title next to it. If you only code, then it's more appropriate to say software dev, or programmer. But, again its highly dependent on your role.

And as other people have mentioned, seems like outside the U.S. the term engineer is a protected title, so my take really only applies within the U.S.

I would say tho, a lot of programmers in the U.S. do get called software engineers. Just depends on where you go I guess.