Thesis in use, potential employer wants to see source code
This can be broken down into two issues:

(1) Can you show the new company your source code/can they ask to see it?

They have only asked to see it, not to use it. Maybe as a way to assess your skill, see if you fit their requirements etc. No problem in sharing this. You could even share a copy of your thesis. If they want to use the code, and say so, you can look into licensing options.

(2) Have you given away your right to share it?

No, because the absence of any written contract works both ways. It is part of your thesis, so it is still formally yours. Until and unless the target establishment tries to copyright it in some form, you have the right to share it.



An exception has been pointed out by David Z - there is a possibility that your advisor's 'tie-up' with the target establishment could constitute a work-for-hire agreement, and this may restrict your freedom to share. If such a case exists, either you or your advisor must be aware of the details and can find suitable redressal. If you were not made aware of this, ignore all concerns and share.



Do get your adviser's consent and guidance anyway, and also check your university policy on IP.