I assume you don't have many miles on your 2012 car? I would have expected all early M3W's to have had their alloy rear sprockets replaced by now but there must still be a few left. Low mileage early cars can require a lot of work and money to make them useable if they have quietly sat in garages for several years. The alloy sprocket will be the reason for the noise and will require replacement with a steel or poly overlay sprocket. It's not worth the effort trying to make a worn alloy sprocket run quietly.
