Assuming you are using a 5v reference, then your 10b adc gets you a theoretical resolution of 5/1024 volts/cnt, or 4.88mV/cnt.
With a sensitivity of 185mV/A, each mV out of your current sensor is proportional to 5.4mA so your ADCs Lsb is equivalent to 26.4mA.
The ACS712 has 21mV of noise, so thats +- 4 counts on your adc.
A suitable averaging function should be able to resolve your 68mA current, but you may well need to use an AutoZero type strategy to get the highest accuracy, as you are dealling with just a few cnts.
If you oversample of ocurse, then you can use that noise to your advantage! Depending on how fast you need to update your current information, you should be able to get at least 11b resolution with oversampling. Alternatively, use a hardware low pass filter on the current sensor, to "average" out the noise floor