A simple but effective method of improving your video quality in low light conditions is to simply lower the frame rate, for eg, going down from 1080/60fps to 1080/24fps, 1080/30fps or 1080/48fps frames per second.
Lowering the frame rate allows you to change the frames from 1/60th of a second to something like 1/30th of a second. The slower speed allows more light into the camera and therefor brightens the image.
The Hero 3+ Black Edition can do this automatically if set to Auto Low Light Mode.