OK, the entire tub of the machine will be coated in this gunge.
It happens with the detergents, softeners and low temperature washes.
You need to do some aggressive cleaning of the machine to get rid of this gunge.
First, with nothing in the machine, run it on it's hottest wash.
This will begin dissolving the gunge.
After 2 or 3 of these, use a washing machine descaler/cleaner product.
This will help get rid of the more stubborn stuff.
Once it's cleaned up, you'll not get the grey stuff on the washing and if you do a regular maintenance wash (cleaning wash) it will help keep the machine clean.
Try it out, see how it goes and get back to me if you need more help.
Hope this helps