I have been using Mobil Semi Synth 2T oil in my H2 for years, also used in my previous MZ and it is virtually smokeless once the engine has warmed up, or you give the motor a big handfull.
When I bought the MZ there was a small amount of fuel in it and who knows what 2T oil it had in it, since sorting the bike out I have stuck a gallon of new petrol in it along with the correct amount of Mobil Semi Synth.
As I rode the bike the smoke cleared so I am hoping that it was caused by the oil that the PO had mixed with the petrol, really should have drained the tank.
It was smoking to the point of embarrasment - it looked like the trail that the red arrows leave behind them but after a few miles it cleared and when I returned home there was just the faintest of blue smoke.
It's all good fun, now lets get that coil changed and new plug fitted, also double check the timing as I have a nasty feeling I forgot to tighten one of the screws.