Text Message Forwarding code not showing up My Mac Mini, running El Capitan, and my iPhone 6 Plus are both on the same WiFi network, however when I select the Mac Mini in the Text Message Forwarding settings, it does not send a code to my Mac Mini. 

If Messages is not running on my Mac Mini, then selecting the Mac Mini in the Text Message Forwarding settings on my iPhone will start the program, but no code. I have signed out and back in to iCloud on both devices, and I have rebooted both devices. Nothing seems to work.

In fact, everything was working as it should until around the time I updated to El Capitan.

How can I troubleshoot SMS handoff from a cell phone to OS X?
Handoff works over bluetooth primarily, so you don't really need WiFi connectivity. Start by toggling the bluetooth on both devices and see if other handoff / airdrop operations work. That will rule out interference and other issues on the basic connectivity.

You do need to be signed in to the exact same iCloud account on both devices, so checking the clocks of both and signing out and in can often verify iCloud account is operational on both sides.