Today I tried to test the Circuit I build. I redesigned it to use only two instead of four secondary coils, halving the voltage to 90V. I also proceeded to adding the N-channel MOSFET as a low side switch to the circuit and pulsed it with a 40kHz 10% duty cycle square wave coming from a 555.
The result was rather disappointing, because I didn't get any spark in the water.
I think I have to read more articles regarding the topic an redesign the circuit.