I don't recommend doing this particular 200k.
If your longest ride was 36 miles, 3 weeks is nowhere near enough time to ramp up to a 120 mile ride. It's barely enough time to acclimate to the heat, let alone quadruple your endurance.
I don't think the consequences would be catastrophic, but you might not finish, get a minor injury or both.
I know 200ks aren't that common, but there should be one later in the year that you can do and will have time to train for properly.