Connecting portable generator with L6-20P to house with L14-30R
Forgot to come back here since there was no answer posted. Appreciate @Harper's help, I wish they would have put an answer so I could accept!

So I ended up buying an L14-30R and replacing the L6-20R in the generator. I wired neutral over to the 240V and wired up the two hots to it. I wired ground over to one of the 120V that had ground on it but I REMOVED the jumper from ground to neutral. 

Since I only have a interlock and a inlet plug for the house, neutral is NOT switched over to the generator. If you have a proper transfer switch neutral MIGHT be switched to the generator. Since neutral was not switched, I'm using the house's NG bond and therefore I want neutral to float in the generator. If you do this, you should label the generator as Neutral floating in case you sell it or need reminding.

Everything worked well when I was running on generator power for 3 or 4 days after an ice storm.