it's silly me

could I please have a guide to obtain a initrd + vmlinuz + modules compiled for i586?
I need it to brew the Porteus-v1.0 to run on my Edubook Gecko from Norhtec.com
It is an i586 compatible ultra low-power low-cost sub-notebook running on AA batteries (yep

It runs vanilla Slackware, but i wanted to get advantage of the lzm/xzm compression speed up when using SDcard as the mass storage?
The CPU is 1GHz and uses just 5W for work, so it's not an ancient "can", but an rather "exotic" hardware, okay?

Best regards,
Stevan C.