what cause grey smoke from 5501 2008 bmw

Most likely it is oil smoke from sitting overnight, it is possible that the valve guides and or seals have worn just enough so oil drains down into the cylinders when sitting overnight so you get smoke on initial start up. Just keep and eye on oil levels. If it is actually white smoke then it can be a cracked head or headgasket and that would be followed by a loss of coolant.