The specs says -81 to 81 mv on the current shunt.
So you can not have more than 81 mv drop on the shunt before saturation of the ADC
You mention few tens of mV drop so say 20 mV drop gives R = U / I == 0.020 / 4 = 0,005 Ohm shunt.
Then you have 20mV drop at 4 Amp.
Benno