The existing asix driver does not support the new AX88772B based USB to Fast Ethernet devices. The linux driver source files found at http://www.asix.com.tw/FrootAttach/driver/AX88772B_772A_760_772_178_LINUX_Driver_v4.1.0_Source.tar.bz2 however do. I have compiled them on Ubuntu 11.04 32 bit using 2.6.38-8-generic kernel and got it working using insmod, but I have not been able to get Fog to load the driver properly in order to image my devices which use this card.
I downloaded the newest Asix driver from the link provided in the request description. I overwrote the asix files (asix.c, asix.h, axusbnet.c, axusbnet.h) inside the kernel source for Ubuntu 11.04 kernel 2.6.38 with the new files form the downloaded driver, and left the Asix 88XXX driver support enabled in the kernel config. When I compiled a custom kernel for FOG, the drivers are now working. I guess I'm just trying to tell you how I did it to save you some time.