Wow, you need a lot of luck! white smoke is sign of burnig oil. That could mean many things.
Turbo seals or bearings giving up and the car emits white smoke.
car loosing compression also emits white smoke.
clunking noise from the exhaust might be a shot bearings and shaft having play or simply you might have a busted exhaust downpipe.
But all these things do not happen by using low octane fuek just once, unless the car was run on full boost all the time.
Or your knock sensor has just come into play and retarding your timing due to low octane.
Like I said could number of reasons, and sitting on a cputer and guessing is not an exact science.