I agree with Larry. It could be poor balance. I got 4 new Goodyear tires recently, and the car shook as out-of-balance, yet the tires were spin-balanced on an electronic balancer. Found someone with a Hunter machine which measures road force (actually rolls the tire under load to check for uniform stiffness) and one new tire got junked.
My 420 was extremely sensitive to shake, to the point it was not drivable at speed, until I changed the steering damper; the old one offered no resistance when moved by hand. Everything fine now.