What else is disconnected when the radio is out of the dash? CAN Bus?
You may wan to try tybalt's suggestion, connect a wire to one of the screws on the radio chassis and the other end to a piece of metal connected to the car body.
Not sure if the radio manufacture customer service can help you out as it could be an internal radio issue.
Check all the connections, a slightly loose connection (maybe a combination of aluminum and coper wire) can give you symptoms like you are seeing.
Here is a link to Crutchfield's noise supression guide: