Admittedly, it's tricky to do, since that name recognition only really matters if you can also manage to publish enough papers. Realistically grad school is more likely for that than during a postdoc or as an assistant professor. Some grad students manage to release some widely used software (well, usually "widely" in a particular niche), which I think does help them build up more prominence than someone in their career stage might otherwise have had.
On a different angle, having produced some reasonably decent software can be a nice thing to have in your back pocket if you ever consider moving to industry. Having N papers and one decent software package is probably a better academia-to-industry transition CV than N+2 papers and no software packages.
I also strongly agree with your other point about just making it open source and if anyone needs it they can get download it and ask you questions.
If you find yourself re-using that bit of code, then it may be worth cleaning it up and making it maintainable. If people start sending you requests for it, then it may be worthwhile open sourcing it, documenting it, maintaining it, etc.--but only if you have time.
I do make open source scientific software as part of my job, but I'm at a later stage in my career and it's not something I would have a science postdoc work on--it's just not fair to them and their career prospects within science...
Recently, someone asked for some reduction code that I've developed and I realized that while it was documented, I didn't have time to refactor it and clean it up--finally, I just put it on github and told them to contact me if they had questions--they were happy to have it as a starting point for what they wanted to work on. So, if you believe that you've made something worthwhile, but don't have the bandwidth to maintain it and other people might find it useful, sometimes it might be better to just put it out there and let people play with it--no guarantees, but it may help someone else get started...
You can get a large number of citations in some subfields for writing commonly used software--but it may or may not help your career. For example, I have friends at various institutions around the world that tell me that their management gives them no credit for developing useful software (complete with lectures, updates, documentation, etc.)--they just release it because they feel they should and most of them are also already tenured in their positions.
Good luck!!!