I think it depends on your comfort level. I have driven 178 for almost 50 years and have seen semis with 45 foot trailers. You will be on lane next to the canyon wall and there are rock overhangs. Some are painted because they have caused trouble in the past. I have seen awnings laying on the roadside from hitting the wall. I towed my 38 foot fifth wheel behind a crew cab dually and had no trouble.
If you are doubtful, the 14 to 178 is a much nicer road. It is a long steady pull from the 178/14 junction to the top of Walker Pass. You will come into the lake area and turn right on Sierra Way to go through Kernville.
