Can't find HTML Snippet in Profiles (Joomla)
You need to enable remote profiles.  Administer menu » System Settings » Misc.  Unfortunately, from your screenshot I see that you're running Civi 4.7.14.  That version has a known bug, where remote profile setting can't be changed.

I would recommend upgrading to the latest 4.7 (this is a good idea anyway; 4.7.14 has known security bugs), then enable remote profile submission.