What can I do to get academic credit/recognition from my hobby project?
What you should do right now depends on the nature of the improvements that you have made:


If your new algorithm achieves its improvement due to some shift in how you represent or think about the problem, then it's probably worth publishing.  You don't need to be in any special position to publish: anybody can write a paper.  Look at where the competing algorithms that you outperform are published, and how they are presented and evaluated in those papers, and you've got a good template to start from.
If your new algorithm is mainly an improvement because of a whole bunch of little tweaks and optimizations, or because of how you've coded it, then it's probably not worth publishing, but definitely worth sharing as a software engineering artifact. It may not be scientific karma, but it's definitely computer programmer karma.


Getting a Ph.D. is a whole different matter, which involves a lot more than just doing a piece of research (though that's certainly part of it).  If you want to pursue a Ph.D., it will be a multi-year process with a lot more scientific contributions involved.  This work that you have done, however, could definitely be helpful evidence of research ability and help you get admitted to a program.