The CLX-6220 is working fine with the 4.01.17 driver installed from Your repo under Wheezy (64bit) - thank You so much, bchemnet!
Scannig via LAN is possible "out of the box", as is printing via USB port. As to printing via LAN, the CLX-6220 obviously does not work with the new ipp protocol of CUPS 1.5.3. (http://www.bchemnet.com/suldr/printing.html#3
). Copying the file /usr/lib/cups/backend-available/ipp14 to /usr/lib/cups/backend/ and then using "ipp14" as protocol when setting up the printer in the CUPS web frontend solved the issue for me.