How to convert low voltage (< 0.4V) AC to DC
Half-wave with a Schottky diode (eg. 1N5817) would give you some voltage at very low efficiency. 

A better way would be to use a step-up transformer to provide more like >10V RMS where an ordinary rectifier or Schottky bridge would be reasonably efficient. 

You have 285mV RMS, so >30:1 would be good. If you can find a 240V:5V transformer that should give you about 14V RMS which can be easily rectified (at 1/50th the current, of course). That could provide about 18VDC which could be converted with a SMPS converter to something useful. 

There may be some chips designed for harvesting energy that would be effective directly at the 285mV level with an inductor rather than a transformer.