Yes...it does not involve C++ at all. Unless by code a website you mean coding the server and everything else as well...but even then I don't believe it is too difficult really.
I'd just started with Wt http://www.webtoolkit.eu/wt/
The main advantage, you will not code a line of html, css or javascript. It's all C++. (or that's what they say)
well, c++ is alot harder to learn than css and html, so i dont know if that is a good idea, if you dont have a background in c++ programming. i am decent in web design, and i have only done html and css for about 3 weeks (had to learn it cause of school)
i do have the support of a teacher, but i suspect i could learn the same amount of stuff in less than a month without a teacher.