BRIEFING: "PREPARING FOR THE INVASION"
Send the Gigalord to colonize any planet in galaxy arm number 11081985, in 806-989 solar systems.

I don't want to turn in my gigalord badge and gain 15,000 rank yet but I want to know if it will actually be able to colonize that far away in decent time or is the quest lying to me? I looked at the time with a ship of the same speed and it shows me some impossible numbers such as: Flight duration: 1477587:28:57 & Vespene needed: 324 478 000. That it 168 years if you don't feel like doing the math. 

My only theory on how to get there is to try for wormholes but if that is the case do I even need the gigalord or can I use normal colonization ships?

You only need to fill the gigalord to max. capacity with vespene then it already works. You won't need 324 million.