I don't think its possible to upgrade the current ship to jump-4. With the required jump drive and power plant upgrade, along with the additional jump and powerplant fuel needed, your into negative cargo space. You would have to gut some of the ship to make it all fit.
Edit: Nope, no gutting needed. The additional 44 tons of fuel, and the larger drive and power-plant (16 additional tons) does drop the cargo space down to 4 tons though. Don't forget to upgrade the computer as well, for the needed jump program. (Model 4, or model 3 with a jump control specialization). No additional space required for that, though. Just money. Roughly 74 million credits total, not counting what ever you sell the old parts for, or any labor charges for the work needed. (Yeah, the class D jump drives and power plant combined cost more then their current entire ship was worth brand new.)