Netlify (free) + and static site builder. My blog (the one this article is on) was built with Gridsome (uses Vue.js). I personally like it a lot.
Other options are, Jekyll, Gatsby, Hugo and many more. Netlify will make any of those free.
What do you mean by "with code support"?
Probably syntax highlighting, as discussed in the article
You can host on Github Pages for free using Jekyll, which supports Syntax Highlighting of code snippets. You can buy your own domain name and point it to your gh pages site.