I am assuming that this is a conventional current transformer, ie a winding on a toroidal core with the main current carrying wire passing through the hole in the toroid.
I also assume that the output (DC) is to drive some instrumentation.
The voltages you quote are a bit (a lot!) on the low side for a simple diode rectifier.
One possiblilty would be to increase the load resistor so that you have several volts to work with, if that is possible.
The other thing you could do is to use an op-amp in a "precision rectifier" configuration.