When I don't activate syntax highlighting, I can set a background color for code blocks like this:

:highlight markdownCodeBlock ctermbg=240

But this sets the background color only until the end of every line and skips empty lines. Example:

Can I somehow achieve that the background color is set from the left to the right window border giving me a rectangle of the defined background color? (Isn't this what you understand by a "block"?) Maybe by setting NonText for this region as well!?

Like this (here faked by appending the right number of spaces at the end of each line):