A high speed shimmy is usually caused by a wheel that's out of balance or a bent wheel.
The first thing to check for would be a bent wheel. Raise the front of the vehicle off the ground and rotate each wheel by hand. If you see any sideways or in and out movement of the wheel, it is bent and needs to be replaced.
WARNING: Although some people claim they can straighten bent wheels, doing so is risky -- especially with aluminum alloy wheels. Replacement is the safest option (but also expensive).
If you don't see any sideways movement in the wheel, it doesn't necessarily mean the wheel is straight. There may be just enough sideways runout to cause a shimmy, but not enough to see. To find this kind of problem, you'll need a dial indicator. More than about .050 inch of sideways runout can be enough to cause a problem.
If the wheels seem to be straight, have the balance of both wheels checked (or rebalanced). If that fails to cure the shimmy, you may have some kind of tire problem due to defective belt alignment or tire construction. Other causes may include loose or improperly adjusted wheel bearings, insufficient caster alignment (check and readjust alignment as needed), or a worn steering damper (on trucks or other vehicles equipped with a steering stabilizer).