Rebmu, 91 characters
Due to the Catch-22 I have to post to get this answer's URL. :-/ Okay, got it.
paTSrd http://codegolf.stackexchange.com/a/28154[th<a name="28154">th<code>cpCto</code>]prC
Rebmu is a dialect of Rebol, and you can read all 'bout it. The equivalent Rebol here would be:
parse to-string read http://codegolf.stackexchange.com/a/28154 [
thru <a name="28154">
copy c to </code>
Rebol's PARSE is a sort of highly-literate answer to RegEx. It starts a parser position of the input (which can be any series, including structural blocks...binary data...or string types). The rules are a language for how the parse position moves.
Tags and URLs are really just strings under the hood in the language. But they are "flavored", and as Rebol is dynamically typed you can check that type. READ for instance knows that if you give it a URL-flavored string, then it should dispatch to a scheme handler to do the reading. (In this case, the one registered for HTTP). You get back UTF-8 bytes by default, so we use to-string to decode that and get a series of codepoints in a normal Unicode string.
In the case of the parse dialect, encountering a tag type is just matched as if it were a string that looked like the tag. THRU is an instruction meaning "skip until the ensuing rule is matched, and then place the match position at the end of what you just matched." (TO is the analogue that matches, but leaves the parse position before the element).
So we zip along past the
<a name="28154">. Then we zip past the next occurrence of
<code>, with our parse position now located right after the
>. PARSE's COPY command then lets us copy data up to another rule, in this case that rule is
[TO </code>]... so we get into the variable C everything up until right before that
Cool, huh? :-)
Technically I could shave more off it, for instance by seeking
TO "</" and that saves three characters--there's no need to match the whole
</code> end tag when just
</ would do. Similar arguments could me made for the start tag. But Rebmu is about literate golfing...even if you might think it looks odd at first!
/body trick is out of the bag, but I'm similarly going to leave it as-is...because I think it is more educational this way.