After we me made the box we could think about the mattress as we had the exact sizes now. Luckily there is a foam material shop right under our apartment! So we bought 5 pieces equivalent to the box pieces, we only made the mattress 3 cm wider to minimize the gaps on the side. Here are the cutted matresses:

Now we had to calculated the amount of material we need for the cover and how to create them. Fortunately I learned how to saw in school and a friend could lend us her sewing machine.
We went to a local fabric store and searched for about one hours until we finally found a fabric we liked and wasn't to sensitive for camping. We picked a black more solid one for the sides and the back and a nice grey/black patterned (in real it's much darker than in the pic) for the top:

And then.. the horror begun! Ok, it wasn't that bad, but honestly I really underestimate how much work it would be. I wanted to make hem washable, so I also bought some zip for the sides.
As I'm still in the progress I will post the final pics when everything is ready :)
Enjoy your travels! soapbubbbbles