Well its been nice knowing you! Nearly all modern direct injection engines suffer with carbon build up on the intake valves. Where the fuel does not pass the intake valves inn modern motors there is no fuel to keep thelr backs clean...that combined with egr valves letting oily air into the air intake which burns onto the back of the valves ruins air flow into the engine. It's gets to the point that the intake ports become so blocked with black sticky baked on carbon that they become difficult to start. Yeah I know you meant carbon build up on the valves inside the combustion chambers and on the valve seats preventing the valves closing....but carbon on the valves is carbon in the valves!
I only recently had to rebuild the head of petrol 2.2 ALFA 159 for just this reason. Of course in the case of this problem it will happen no matter what grade of fuel you use.