there is a way to run homebrew and unsigned code, but you will need a virgin 1st gen (not elite either)console with no updates. the hypervisor exploit was patched ,but it is still a viable option if you got the pristine hardware.
the problem is that the console demands that the firmware match the title, for example a new game wont on an old system kernel. so while you may be able to run linux on a hypervisor capable 360, you would be limited to first string release titles.