Hum...let's see. I've been writing code for a living for about 22 years now. When I went to school they taught me Fortran and Pascal and Lisp/Scheme and Assembly and this new fangled language called C.
Nobody ever paid me to write Fortran or Lisp or Pascal. They did pay me to write C, and sometimes I had to resort to assembly language for certain problems. But I don't get paid to write C code anymore. I moved on to C++. Then C#. And Java. And JavaScript. And SQL. That's what I get paid for today.
I didn't go back to school to move along. Once you learn the art and science of computer programming, picking up a new language isn't all that hard. That is what you *should* learn in school, but sadly all they usually do is teach you a few programming languages.
Whatever you learn about computing in college...it will be obsolete *LONG* before you retire. You will need to learn new things. Or you will become a Dinosaur. I've seen lots of programmers become Dinosaurs. It's not fun to watch. Dinosaurs refuse to learn new things, and they don't really need to, because they have an important job and they can't be replaced. Or so they think. Then the system gets replaced with a new one, and the Dinosaurs are lost. Or unemployed. And they have no skills that anyone wants today. I've seen it happen, too many times.
You don't need to go into management. Many software engineers make truly awful managers. I'm a good SW Eng. I would suck as a manager. They are different skills.
Bottom line though...yes, you *HAVE* to keep learning in this business, or you become a Dinosaur. Very quickly. Don't let that happen to you.