I figured out that the issue even exists if the aluminum frame is touched. From my opinion because of that the solution to remove the case is only reducing the frequency of the occurrence, it does not finally solve the problem.
Anyhow I don't use any case or cover.
I will return the phone and get my money back. I'm very sorry about that because I have been waiting for the phone to replace my old Xperia ray for nearly one year.
This touchscreen bug has been discovered on Xperia Z and Z1 and z1s, now the same error applies to the z1c. Sorry Sony, I will not buy an Xperia phone anymore.