If the wheel is torqued to the hub at the proper spec, you have a few culprits to consider,
A Bent wheel, as YGMN mentioned
Tire out of round radially (heavier across the width of the tread in one spot as opposed to another. this is easy to balance out), also as YGMN mentioned
Inconsistent tire sidewall stiffness (most often occurs on lower quality tires)
Although not common, the wobble could be from a wheel bearing wear or failure
Tire out of round laterally (when a "patch" of the tread is lighter or heavier than the tread section adjacent to it ie. there is a heavy spot in the inner half of the tread compared to the outer half of the tread at the same point on the tire. This can most times be balanced out if not too severe. Being able to correct this also depends on how deep the lip on your wheels are as w/ "deep dish" wheels, you can not weight them on the outer edges) I think that this is most likely the culprit. (most often occurs on a low aspect ratio, wide tire). With a low aspect/tread ratio, a balancing of the tire at the original mounting is not always able to keep the wheel/tire balanced for the duration of it's wear lifetime. As the tire wears, heavier spots may be worn off and since the vast majority of the weight on a 305/40/22 is in the cross section, not the sidewall, periodic re balancing is necessary, if not done, the shake you are feeling can develop. I balance my 305/30/26s every spring. I don't run the highest quality tire, but not a cheapo either, and although the shimmy is non existent, you'd be surprised at how much the weight gets moved around to re balance them.
