Well, You could do that but like they said above, You'd be giving away 4 years of training at a VERY high tuition cost You already spent.
There IS a way however to actually impress a potential employer WITHOUT giving away services they might actually be selling.
You can pick up a used cheap laptop or netbook, install a webserver OS on it (Because You have the CS degree also), & then create a few hundred websites on it - complete with Your own customized scripts in any languages You know (Java, JS, Python, etc.) that can be carried with You to a job interview to access by the employer directly. You can decide which sites they look at during the interview that showcases Your abilties relating to their questions directly on the hardware.
You can also accomplish pretty much the same thing simply by running an old desktop on Your home internet for the same thing & simply carrying a cheap tablet with a good size screen (a 10" tablet runs about $90US these days) that they can use to access Your personal server - again, by whatever they ask You during the interview & with their company's WiFi.
If You're going to do something for free, remember that whoever You do it for couldn't do it themselves in the first place, & if they have to fix it, guess who they call first - still expecting the fixes for free.