Let's take the sample items from a prominent study by Friedemann Pulvermuller et al. (2005, Functional links between motor and language systems. European Journal of Neuroscience, 21: 793-797). This is a TMS study that found faster lexical decision RTs to hand/arm words when hand/arm areas were stimulated, and faster RTs to leg words when leg areas were stimulated, etc.
So here are the sample arm words: fold, beat, grasp.

The verb beat is no better. I can beat an egg with a fork or a hand-held blender, and I can beat an attacker with any number of actions (punching, hitting with a bat, kicking, sitting on).
Likewise, grasping can be achieved with a hand or a tool or a mind, as in "Language within our Grasp." Consider as well, that if i reach out to grasp a glass, but the glass is damaged and shatters in my grip, I did not grasp the glass, but instead crushed the glass. So the same motor action can lead to different conceptual action.
The situation isn't much better for the leg action example words: kick, hike, step. Hike in particular is odd in that motorically it is identical to walk, the difference being in the purpose of the excursion not the motor codes at all.
In other words, a specification of motor codes is not going to get you very far in capturing verb meaning, even for these cherry-picked examples.