Asko 620 washing machine keeps filling

Sounds like your fill solenoid has stuck in the open position. There are 3 #20 Torx fittings along the back and you can lift off the top panel. The solenoid will be in the back left side.

I would shut off your house water supply to the machine and then do a voltage check to see if the solenoid is remaining energized. Another more simple option is to give the device a few light taps as some debris may have become trapped inside and caused it to become stuck open.