I had written a small tool for pico8, but it is written in pure basic and the resulting program is a nativ windows application.

Is it allowed to present this tool here with a link to a github-page, including the source code, the binary and how to use it with pico8?

I would say: Sure. Other people had already done this, for example the Creator of P8Coder: https://www.lexaloffle.com/bbs/?tid=3351