When you double-quote a path, you’re stopping the tilde expansion. So there are a few ways to do this:
cd ~/"My Code"
cd ~/'My Code'
The tilde is not quoted here, so tilde expansion will still be run.
cd "$HOME/My Code"
You can expand environment variables inside double-quoted strings; this is basically what the tilde expansion is doing
cd ~/My\ Code
You can also escape special characters (such as space) with a backslash.