Modern washers have some pretty sophisticated controls. Not unheard of for them to be noise generators. Even with the washer not actively running, the control board still is powered and is waiting for button presses.
A good test would be to unplug it and see if the noise goes away.
All of this is covered under Part 15 for "unintentional radiators". Many non-radio electronic devices, like computers, will have a Part 15 notification buried somewhere in the manual. It'll say something to the effect that the unit cannot cause harmful interference and must be able to handle interference without causing improper operation. It'll also say something to the effect that if it does, move the devices farther apart.
The receiver in your amateur radio probably has a part 15 certification also.
Solution is to move them farther apart. If it's a big issue, complain to the manufacturer. Or, look for someone who's had this issue before and can give you some pointers on how to address this. I'm lucky enough that my early 90's washer/dryer set is still going strong with occasional repairs. The electro/mechanical timers don't usually generate any noises.
If you want to see some real headaches, search on amateur radio operators getting interference from LED light bulb and flat screen TV sets.
