I live in South Carolina so the absolute coldest we see is upper 20's in the dead of winter and I don't ride then anyway. My local Walmart has 10w30 full synthetic atv oil. That's why I was wondering about synthetics with the dct.If its not cold where your at get 10-40.
I'd stick with conventional honda oil or something very close to it.
The DCT is basicly an auto car transmission, they're fussy about what oil weight you run. If it was a foot shift I'd recommend rotella 15-40.