Driver selection

14V/20Ohms = 0.7A capability with flyback

If the two coils have independent magnetic paths (which I expect), low voltage flyback is the best. Either:

If the 2 solenoids have the same magnetic path (very unlikely, only unipolar steppers have that), than high-voltage flyback (16V or above, 18..20V recommended) needed instead of low-voltage flyback: