So basically a lot of MUSHes are running their own "codebase" in a sense.
(Probably you could just read what @Rook wrote several times to greater benefit, but here's my bit anyway.)
No, not really. I think part of why some people are becoming frustrated with what you are saying is because it is hard to communicate past your misconceptions.
TinyMUD derivatives like MUSH and MUX (and I think MUCK and MOO as well, although I don't really know how much game-specific content the various MOO Cores) are both content-free and content agnostic when you start them up. Their codebase is nothing more than the collection of mechanisms that enable them to start up, have characters, and have rooms, and allow connections. So, saying that "a lot of MUSHes are running their own 'codebase' in a sense" is really just a misapprehension of what's happening.
Likewise, MUSH is not a genre. A game's genre is concerned with elements like setting, whether conflict is primarily PvP or PvE, and so on. MUSH (from my non=coder's perspective) is more like machine code than it is like an operating system or even an application. Looking at it another way, mystery stories are a genre. Those stories can be created as films, television programs, books, and plays. To think, however, that books are intrinsically mystery-telling devices and to ask a fantasy author, "What kind of mysteries do you write?" just produces confusion and in the end doesn't really tell you much about stories, writing or books.