Tervan do you have FTP acccess to your domain? If you do (and know how to access it), one way to get past the problem you are facing is to manually delete the askapache-google-404 folder from your plugins directory via FTP.
This will allow you to access your admin/back-end again and then you can install version 220.127.116.11 and get things running again.
That is what I did and I haven't had any problems (even my settings seem to have been saved somehow - maybe they are stored in the WP database? Not sure). Please be warned however that doing this may result in loss of your previous settings/customizations for the askapache-google-404 plugin.
The other guys will probably be able to provide you with a more "delicate" way of disabling the plugin, but removing the old version of the plugin entirely worked for me so I'm sure it will be fine for you. Since there have been quite a few updates to this new version of the plugin you would probably have to go through most of the settings again anyway just to check, so if you do lose them in the process of sorting out this problem it's not really gonna be an issue.
Anyway - good luck. Hope you can get it sorted out without any unnecessary hassle.