For faster feedback on the core ideas, a paper would serve very well. You'll have the attention of your peers and the faculty to gather initial impressions.
There isn't any reason why you couldn't do both. Open sourcing new ideas doesn't mean you cannot write a paper on the subject. The code is still your idea at the core. Refinement of the code doesn't change that fact.
One paper rarely does anything. Likewise one repo. Certainly each can point to the other which may help someone else to understand what you were trying to accomplish, and hopefully build upon it.
Regardless of all of the above: making a public repo with an open source license is a good thing to do if the alternative is for it to be dropped. Back in the early 80s I wanted to see some code written by one of my advisor's prior students (for his PhD) back in the late 70s. I had to send him email to Sweden, where he had since gotten a faculty position, and he sent me a tape! His code was no longer on MIT backups. All this for what turned out to be me reading a few functions our of his implementation that explained something I hadn't understood in his thesis. Had I known, I could have just asked him the question. Or today, looked at the code on GitHub.
I think you may also get some satisfaction in writing up your work. You can store the paper in the repo as well, of course, in addition to submitting it to a journal or giving it at a conference.