Advisor wants copy of code to give to other student
Should I flat out refuse to share it and make Jen develop the code on her own (given there isn't an immediate paper deadline pending)? 


What would be the purpose of this?  You'll upset Jen and your advisor, she'll have to spend time redoing what you've already done, and you'll have substantially decreased the usefulness of your contribution with no corresponding gain to anyone.  The only reason I see is a feeling that Jen is getting away with something and not putting in enough work herself, but I don't think you should be concerned with this.  Your advisor is aware of the situation and should ensure that she does enough work to justify awarding her degree.  Maybe she is doing great things you are unaware of.  It's also possible that she won't end up doing as much as the average student, but that's OK: she'll still deserve the degree, but just won't get strong letters/references.  By contrast, you'll get glowing reports of how you not only completed a substantial project of your own, but also stepped in to make major contributions to an unrelated project and ensure that it met a deadline.  That will put you in a great position.


  Should I question the request?


I don't see a purpose to questioning it unless you might plausibly refuse to share the code.

One option is that you could propose continuing to collaborate on this topic.  However, you'll have to handle it tactfully.  For example, it would be awkward to try to use the code as leverage to force a collaboration (by saying "I'd rather not give you the code, but I'm happy to make further changes if you let me know what you need"), or if it comes across like you are cutting Jen out of the project by offering to play her role and suggesting you would do a better job of it.  If you'd like to collaborate, it's reasonable to say so, but you should be open and collaborative, and make sure to allow everyone an opportunity to contribute.  (And it's best not to let this distract you too much from your primary project, since you'll have more to gain from a project you have greater ownership over.)