LC circuit powered by MOSFET generates not stable
Q1 probably needs to have a little bit of DC bias in order for it to start oscillating so, I suggest that pin 6 of the transformer (as shown in your diagram) is raised by a small DC voltage in order to take a few tens of milli amps through Q1's drain. Try using a potential divider - maybe 10 kohm and 680 ohm. The 10k would connect to 30 volts and pin 6 and the 680 ohm from pin 6 to ground.

Bear in mind that these are approximate values and not calculated. I would also urge you to use a simulator to try and get it working with the "better" values. You might also consider reducing the amount of AC fed back to the gate because, when it is optimized, given the same turns are used on both primary coils, there will be too much positive feedback.

See also this question and answer regarding a tuned collector oscillator and fixing it to produce a cleaner sine wave - it's very similar to your set-up so it will help you understand the importance of restricting the positive feedback levels in order to produce a decent sine wave.