Like this:
name=$(date '+%Y-%m-%d')
tar -zcvf "$name.tar.gz" code
or even in one line:
tar -zcvf "$(date '+%Y-%m-%d').tar.gz" code
Drop -z flag if you want .tar instead of .tar.gz.
Use %y instead of %Y if you want just 2 digits of a year (17 instead of 2017).
$() is used for command substitution.