Maf's dont always sets codes when they go wrong in my experience, they either work or mis report what they are seeing passing through them or fail completly. Had an issue with mine on the Z3 1.9, car ran but felt restricted when driving it and fuel trims high, unplugging it made a slight difference. Also had a camshaft sensor code, that was changed but in the end I shelled out on an oem Maf, put that on and the car was transformed, no problems since. Its very easy to throw parts at a car that hurts your wallet without fixing the problem, since you got it to start with the Maf unplugged it will revert to default settings instead of reading what the sensors are picking up hence the better running as its ignoring out of kilter readings from bad sensors. Always good to view live data in diagnostics if you can, view what the Maf is seeing going through it at different revs and look at the fuel trims to see what they are doing, high trims are usually down to air leaks in the vaccum system between Maf and exhaust. A visual check of all rubber hoses between the Maf and exhaust side of the engine for splits or holes should be the first thing to check for. Unmetered air not seen by the Maf will cause it to think its running lean and add fuel to richen the mixture hence the high fuel trims. This is picked up by the O2 sensors in the exhaust a mismatch between what the Maf has seen and what the exhaust sees affects the fuel trims. Seems replacing the Maf on yours is the way to go, cleaning the old one with Maf cleaner didn't work for me, it killed the Maf completly.
Do not be tempted to replace the Maf with cheap ebay ones, they rarely work or work for long only buy Bosch or Seimens brands that were oem parts, been there done that paid twice bu got my money back on the cheap part thank goodness.