I've seen in other threads that you can deposit a booked HGVC week with independent exchanges like SFX, which has an agreement with HGVC. I don't think I would due that with the week mentioned by OP. On the other hand, there are other independent exchanges that might be worth exploring, in particular ThirdHome is one that can get you very good exchanges into vacation homes or other high-end TS. I have been using them with some other TS I own (Vistana, Vidanta, and WorldMark) and have started seeing some HGVC ones show up in the availability. They don't have an affiliation with HGVC so you wind up having to get a guest certificate when someone takes your deposit, but that isn't much of an issue for a home week.
Bottom line - what others have posted in this thread is absolutely right for using exchanges directly affiliated with HGVC (i.e., RCI or the HGVC system itself), but things can work differently with others like SFX and ThirdHome.