the last time we were there, a couple years ago, we went up it and there is a BIG sign at the bottom of the cliff with big letters stating length and width limits.
I do not have a picture of the sign, but it definitely rules out your rig.
there is a rock overhang along the road that your rig can't get under and there won't be enough room for you to pull over to avoid it.
P.S. I found a picture of the latest sign:
it does not state length or width restrictions, but the State of Utah road info says this: "The State of Utah recommends that only vehicles less than 28 feet in length and 10,000 pounds in weight attempt to negotiate this steep (10% grade), narrow and winding road. Most vehicles can travel the route safely. Caution is advised for motor homes or vehicles pulling trailers."