Gray water and sediment in hot water after leaving house for weeks

We have a vacation home in the country. If we are away for a week or two, when we return, the hot-water in the house turns gray and has black particles in it. If I flush the tank (or run the hot water for 30 mins) it clears up.

So... I bought a brand new hot water heater and installed it last month. I showed up on Saturday, ran the hot water... gray with black particles.

Now, the hot water tank is DIRECTLY below the bathtub, and the pipe can't be running more than 8 feet, so it isn't the pipes. The tank is new, so it isn't the tank, but the same water is going into the cold water tap, so, somehow the hotwater tank is turning the water gray!

I'm at a loss.

I just bought a sediment filter
( http://www.amazon.com/gp/product/B000E78XH6/?tag=skimlinks_replacement-20 )

Maybe that will help, but now I think it may be some kind of chemical issue, where the heat is doing something to the water.

Any ideas?

That filter won't help a bit.

Are you on a well? Do you know what minerals you have in your water? Do you have any other filtration? How old is the plumbing? What is it, copper, pex, galvanized or what?