When shooting indoors with available daylight, presumably from windows and skylights, at 24p and 180 degree shutter, make sure you have not engaged any neutral density on the filter wheel and additionally you can get an extra 2/3 of a stop by using "electronic daylight correction" instead of the daylight filters. This feature is accessed from the menu. See "Camera Settings" on page 1; use "Daylight" instead of "Tungsten". If still not enough, you may invoke some gain, but as we all know the Varicam is notoriously "noisy" so I usually limit gain to +3 or +6 in a pinch. Of course, daylight balanced lighting like HMI's or 5600 degree Kino Flos are made especially for this scenario.
I think you mean to say "increase" the shutter, meaning opening it up more to let in more light. The conceit is to imitate the motion of a motion picture camera; turning the shutter "off" gives you a 1/24th of a second exposure and each frame has to much motion blur (depending of course on how much motion there is). Also, some motion picture cameras have "variable shutters" and allow you to open up of close down for effect. 220 degrees is often used to get a little more light, but in reality that only gives you less than a quarter of a stop, but maybe that's enough (?)
Also, you must consider how you're judging the exposure; typical LCD monitors exhibit a "false brightness" and computer monitors (in the edit room) have their own particular "gammas" with Apple and PC platforms being different (PC darker). The most accurate measurement is a proper waveform scope, where skin tones can be set anywhere from 40-70ire depending on effect. Personally I set my shin tones at 50-60 rather than let the highlights on the face go white when set to 70. It's really a matter of taste.