Ok, this is gonna be an explanation and a half, so i hope you're ready.
Well, first off, the 'grain' you're talking about is called digital noise, or just "noise" when you're talking about video. Film grain is different than video noise, though they look similar.
Now, on to your problem. These digital video cameras are great in low light, but you have to expect some digital noise, especially once you start using the digital gain.
Think of it this way: On many digital still cameras, you'll see the description "3x optical, 10x digital." What that means is that you'll get three times the magnification using actual physical portions of the lens. Once you go past that, the camera will automatically switch over to the digital part and magnify the image digitally in the camera.
To translate this to your problem, your Xl1 uses two basic ways to get light through the lens to the imaging sensor chips (the CCDs). First, it uses the iris, then it uses 'gain.' The iris is a physical piece of metal or plastic, very similar to the iris in your eye. you can open and shut the iris to let more or less light in, all according to the f/stop. f/stops are the numbers you see on the side of the lens (i.e., 2, 2.8, 4, 5.6, etc.), and these numbers correspond to the opening of the iris, and thus, the amount of light that gets let in. Once you reach the maximum aperture (opening) of the lens, the camera can take over and "boost the gain," meaning it will take the image and brighten it by a certain decibel level. That's what the dB level is.
So, in order to avoid all that noise and still get a properly exposed image, you need....drumroll please....LIGHTS!!!!
That's right. That's why on movie sets you'll always see big ass lights everywhere. You need to actually light the subject in order to see it. Go figure. There's a whole section on lighting here at studentfilmmakers, and there are many, many books available on the subject. However, why not just go to a local hardware stpre, get a couple extension cords, some $30 work lights, some small spot lamps, and light away? You'll have a masterpiece in no time.
Chris