Can the built-in highlight shortcode be overridden?

I’ve attempted to create a layouts/shortcodes/highlight.html file and use it via the code fence, but it seems that this shortcode is not used when I’d like to use it via code fence? Is there a way to have my tripple backtick code fenced parts go through custom templating?

It seems that the closest I can come to this is with using a render hook (see Markdown Render Hooks | Hugo). This does seem to do most of what I’m looking for. However, the context seems to be missing .InnerDeindent, only providing .Inner.