Even as a CS major, the classes you take may not give you enough to do to make you a good programmer. If you want to work with code a lot in the future, you should always have some project/software/app/whatever that you're working on. Plus this gives you things that you can talk about in an interview when they ask you about projects you've worked on in the past. If you contribute to some big open-source effort, you can put it on your resume as well.
Really you don't need classes to help you be a programmer, but of course certain classes help you with some specialized fields such as scientific computing or computational physics. They're generally not the typical CS programming classes, though (they're things like applied numerical methods, networking, parallel algorithms, etc.). Since you have to take a programming class for your engineering major, you could start there and then just learn on your own for the more advanced things.
It probably won't make a big difference that you don't know how to run highly efficient simulations on a supercomputer if your intended field isn't very heavy on the numerical stuff. Still, knowing how to program really well makes for a hell of a fallback plan; writing software is pretty fun.