You're describing what could be severe misfire issues, or more likely boost oscillation, which can be caused by a number of things.
Was the car ever modified? If so, what was done to it?
87 octane should never be run in the car unless it's an emergency and you need to limp somewhere. It does not have enough detonation resistance for a turbocharged engine. It could be that the gas is preigniting causing detonation which can cause engine damage, but that doesn't seem like it's the probable thing.
I would take it to a trusted mechanic for a good once over. Get the plugs changed, the fuel filter replaced, air filter, engine oil and filter and maybe even a coolant flush.
Do you have maintenance records of what has and has not been done? How many miles are on the vehicle?