Vibration during a certain speed

This vibration only happens occasionally and usually at around fifty km/h and seventy five km/h. When accelerate hard the vibration goes away. Only happen when gently accelerate and when reach speed around fifty to seventy five km/h the vibration comes on.

Letting go the accelerator the vibration goes away.
And yes there is a check engine light ( code p0031 ).
Is it possible that this is related to the code?

And I notice that when accelerating full from a stand still, it seems to hesitate shifting in to the second gear.
I than put it in "N" and back to drive before it shifts up.