I have a I4 turbo DI 2.0(LNF) 30K mi and the carbon problem was pretty bad. I discovered this when I inserted a boroscope thru the intake and took a peak at the valves.
Problem is solved! I simply took a 16 oz water bottle poured 1/2 out and then filled with hydrogen peroxide, so I had a 50/50 solution. Started the car inserted a funnel onto one of the vacuum lines and slowly, very slowly poured the whole bottle in thru the vacuum line. Car did not smoke at all, but took a good 15 minutes of easy driving to get it to run good again...then I kicked it in the [censored] and I knew it was clean. I further verified with a boroscope check..what I saw was very impressive, not only was the carbon gone but my valves were shiny and glaring at me, looked brand new.
I did the same thing to one of my other cars with 185k mi and had the same results. It fouled a plug on that one though. The plugs were due for replacement anyway. This was a port injection and was really bad.
It's really a pretty easy maintenance step that all cars will need sooner or later. Looks like every 30k on DI.