You can offer special member registration via an invitation code or a password with the simple membership plugin.
The following steps will show you how to set this up
Step 1) First, create a new registration page where you will use the invite only registration.
Step 2) Use this feature of the plugin to put a registration form for your special membership level on this newly created registration page.
Step 3) Select the password protect option for this page and set a password (this will be your invite code) for it.
You can password protect a page by editing the visibility option of the page. See screenshot below.
Step 4) You can now share the URL of this special registration page and the invitation code with the users.