An op amp connected as a trans-impedance amplifier will convert the current to a voltage. A 10 megohm feedback resistor will give a peak output of 0.3V. You can then voltage amplify that with a gain of 13.3 to give the desired 4V peak.
The op amp must have a small input bias current (probably need to have a FET input) and gain-bandwidth sufficient for your signal bandwidth requirements.