Firstly, magnetic force is a linear function of Ampere-Turns ie amps time the number of turns of wire. So the answer to your question is AMPS. You either need more amps, more turns or both. Of course adding turns means increased resistance so to keep amps up you also need to increase voltage. You say your coil is 150 ohms. That is way too high to get a decent force from a 6 volt system. You should be looking at a pulse current in the order of several amps, which at 6 volts implies a resistance of around 1 to 3 ohms. So, a lot thicker wire required. You also need a hefty battery, something like a small car starter one.
Secondly, you need DC
Third, don't even think about using mains power - you clearly do not have the knowledge (and I'm not being disrespectful)