'A bit grayish' seems to describe oil burning but, as sarabande is suggesting, it could be steam from a water cooled exhaust. A bit more information would be useful, e.g. does it consume oil? Does it start and run well?
I had a Mini-Twin that made those sort of smoke signals. The fix was very simple but I can't recall the full details. In essence, as I remember it:
There is a pipe that carries a certain amount of water direct, across the top of the engine, to the cooled exhaust; whilst the rest of the water is directed through the engine. This pipe was clagged up, causing the exhaust to run hot.
Of course I could be totally wrong about the function of the pipe - but unbunging it certainly cured the problem. I hope yours is as simple.