Copyright differs a lot between countries. However, here I'd recommend to come to a mutual agreement without thinking about copyright fights in the first place.
That is, try to convince instead of trying to win a copyright fight.
In my experience, in academic context some strong arguments for FOSS licensing are
Reproducibiliy is becoming more important. And this includes calculations. Questions about correctness can easiest be answered by "look at the code".
The academic currency are citations. It may be much easier to convert a software into citations (by requiring users to cite you) than into money (this requires a whole lot of infrastructure)
if it is a larger software: in academia people change institutions fairly often. FOSS licensing is a way to make it clear and legal that you have the right to maintain (and use) code even after you leave that university.
If you stay in science, this makes a steady state of technology clear and legal: when you change institution, your new institute profits from the work you bring, and your old institution can profit from the fact that you can still look at this work. You profit by not re-writing wheels.
can I run the code for other people in exchange of co-authorship for their papers?"
Only running code IMHO is something that would be acknowledged, but it isn't enough of a scientific contribution for becoming co-author. So: No.
However, what you can do: write a paper and require users to cite this paper.
A few points about the German copyright in this situation:
Copyright for computer programs is the one topic where German copyright is similar to the UK/US copyright systems.
Basically, if you write the program in order to do work related work, the right of use automatically belongs to your employer (i.e. they automatically get a license), and your wage is considered to include the appropriate license fee.
In Germany, It doesn't matter where and when you do the programming (it can even be in your spare time at home), what matters is whether it is to "fulfill the tasks and directives [of your employer]"(rough translation from the court decision). IMHO the employer doesn't need to specify that you should program this, it is enough that you decide to solve the task he assigned you by programming.
This is different from UK/US I think, and of course it doesn't apply to programs that are not related to your work.
However, things can be different in academia. Lots of German PhD students have working contracts that do not cover the scientific work (the work for hire is looking after lab practica, teaching seminars, etc.). In that case, IMHO the university doesn't hold the copyright automatically.