I don't believe that there is a way to get techapod specifically other than finding it on a planet and mining it (either on a core world, or via the Hydroponic tech for a colony world). 

Otherwise, you can buy it from the Bazaar, if it's available.  

Conversely there *might* be a starbase "rare resources" mission that can acquire it, but someone would have to confirm this for me - I'm not sure which random resources are actually generated from these missions.

Like most of the rare resources, it can be tough to find... 

Hope this helps,

-tid242

edit:  you can always trade an alien AI for it.  If they have a bunch, and your diplo isn't too terrible, they'll usually give it up pretty easy...

In my current game, one of the minor races (the ones that can't be conquered through planet flipping) gave me a "quest" when I interacted with them. Once I completed the quest, I had a choice of rewards and one of them was 0.2 techapods per turn! Lets just say, I'll protect them to the end

Absolutely!