The Betula bookmark manager and the Mycorrhiza wiki engine are among my favourite apps. They both use mycomarkup and are easy to self-host. Give them a spin.
Do you happen to know if it supports tabs in code blocks (renders tabs as tabs instead of spaces equivalent)? I failed to find a way to test without installing.
It does seem render TABs into TABs, yes. However, I don't think you can specify the TAB size. I looks like it's hardcoded to display as being 8 SPACEs wide.
The author, bouncepaw, is very friendly. If you need a TAB to look like it's, say 4 SPACEs wide, perhaps he will accept a feature request.