A gain of 44dB tells me that you are using 1k ohm resistors at R5, R3, R23 and R21.
If this assumption is correct, then to obtain the same gain from a .37mV input, a gain of 56.72dB would be required.
Jim can correct me on this, but you would need to change these resistors to 473 ohms with 475 ohms being the closest 1% tolerance standard value.
All of this is assuming you are using stock parts. If you change the opamps to something other than opa2134pa then you would have to recalculate everything from the start.