Complete circuit:
Bleh, two chips to make the double pulse waveform... oh well, a 555 is too slow. (I didn't even bother trying to test one, so I don't honestly know if it is. :-P ) CMOS is also finicky with high Z and ESD crappiness, but the circuit shown seems to work, so long as you don't get your parasites all over it (a touch's parasitic R and C, that is). The two video transistors do a reasonable job of amplifying the output for the ZTX dudes, which move the MOSFET gate by 10V in under 50ns (longer with load).
Output waveform is complementary of the generated pulses, plus some ringing. At the drain, the Lpulse rings as a result of flyback when the FET is off, while "output" (sans coupling capacitor) rings when the FET is on.
Waveforms:
Tim