More than "minimal", "working" html, css etc is probably a ranking factor - if not directly, then via good UX.
"Minimal" is a somewhat problematic attribute in my opinion. In some context, you can have really minimalised code; in many contexts, best practices should be applied - if only to better maintain code, markup etc. Sometimes you do face technical or ressource restrictions and sometimes, non-minimal practices are just better. (All-time favourite: A certain wordpress plugin that minifies code, in theory speeding up loading time; in practice it oftentimes quadruples the loading time due to its own execution. Nothing won there.)
Moz has now taken to see small markup as a spam signal (whyever) - one of my pages gets the warning that "Site Mark-up is Abnormally Small There's a high ratio of visible text compared to HTML, JavaScript, etc."
Well yes, it is self-coded and has pretty much nothing that is not needed, making concessions only for having source code that is readable by humans as well. This should for sure not be seen as a call to make bigger source code when it is not necessary.
TL;DR: Clean code without unnecessary stuff helps in maintenance and with finding errors should they appear; more than minifying code, I'd worry about page speed and functionality.