Low-Frequency Magnetic Transmitter
The first, obvious, problem is that your new schematic has the 2N6804 connected wrong, with the source and drain reversed.

Second, your 7406 inverter is an open-collector buffer, and requires a pull-up resistor to +15. Try a 1k resistor. Without it, the upper gate never gets driven very high, and the FET never gets turned off very well. Check Q2's gate voltage, and you'll see that it is nowhere near the levels of Q1.

However, even with a pull-up resistor, you won't get very fast transitions on Q2 due to the gate capacitance. Try something with more oomph than a 7406. You might lower your pull-up resistor to about 500 ohms, but less than that will exceed the recommended current levels.