Only you know if 600mV is too weak?
If you think you need a gain of 4, you can either build a single-pole passive high-pass C-R filter followed by a gain of 4 opamp, or you can build a two-pole active high-pass filter using the same opamp with a gain of 1 to ~100. Or if you need steeper roll-off, you can build a four, six, eight, ... pole filter using two, three, four, ..., opamp stages.
What exactly are you trying to do? Gain required? Cut-off frequency? How steep a transition from no-pass to high-pass?