Matrix 02
What you can do to improve it is some testing on an open range/field and change the antenna length and location. Right now, your antenna is too long to be an optimal antenna. Should be 0.25*11,803/440 = 6.7 inches if it was a simple monopole antenna (one wire straight up from a metal disk ground plane). I guarantee you that you're using a very crappy antenna.
If I were doing this, and I've been an antenna engineer the past 20 years, I'd try this.
1) Change the wire to a wide wire brade, maybe 2" wide x 10" long. (wider wire/braid gives better bandwidth and is friendlier to mounting near metal objects). Solder your antenna wire to the braid (i.e strip your wire to make it bare,then solder to braid, only need to connect it for and inch or so). Position the unit&braid antenna so the antenna sticks up or down and as far away from another vertically oriented object as possible. Your present location maybe strong backwards and weak frontwards based on your description. That may be ok if you know how to orient your bike when you park.
2) Go to a field or a slight valley with a friend who has a bike too (he'll need to drive around to test at all angles). Test for range. take at least four measurements when doing range, north, south east and west. You'll find one is up to 4x further than the other. It'll help orient your bike if you know which direction you'll be going after you park it.
3) Fold up the braid to make it shorter and duct tape it shorter in one inch increments. Like rolling up a belt. Then retest for range. Hopefully all ranges will be getting larger, some are likely to slightly shorten, so don't worry about that. Both your antenna pattern and it's efficiency will change as you change length. When you find the optimum, you can just cut the braid to that size. I'd tape over the braid so it doesn't short out to your bike's metal, or maybe coat it with some polyurethane.
You could try a different routine, (just use the wire that's on the unit and fold it up) just vary the antenna size and location and test for range. You could also get a multi section rod/pointer to use as a variable antenna. I've purchased them for $3 from a hardware store. The optimum bike location for the antenna is top of fuel tank, braid/antenna standing upward, but that would look pretty ugly. Don't lay the antenna along any metal, it must be by itself, at least 3 inches from metal oriented in the same direction.
Also, describe the unit and how you locate it. i.e. unit is 2"X4" battery operated mounted on tank. Cable from the unit to the antenna, or antenna connected to the unit's housing.
Kevin