Without knowing what codec you are currently using or your deliverable it's pretty hard to make suggestions. That being said, take an uncompressed version of your file(looks like you already have that made) and bring it into Media Encoder and mess around with the Quicktime H.264 settings.
The big setting to play with is the bit rate, that's going to make the biggest difference in quality/size. Off the top of my head, start around 12Mbps and move up and down from there.
Johnny Cuevas, Editor
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.