XenithOS is a POSIX-conformant, Unix-like operating system with a BSD-like architecture. The kernel, bootloader and user space were all designed and built in-house, and it is designed as an alternative to Linux and the BSD family. The operating system is licensed under the copyleft GPLv2, with system libraries licensed under the LGPLv2.1. Both of these licenses can be found on the Free Software Foundation website, as well as opensource.org.
It is easy to contribute to XenithOS. All you need to do is find a part of the operating system you think could be improved, make those changes, and submit them as patches to the XenithOS mailing lists.
Alternatively, if you just want to explore the code repository, it can be found at this address.