I think you're right, my kernel is 32 bit - i686, I'll need to find a 32 bit miner.
Linux ubuntu 3.11.0-15-generic #25~precise1-Ubuntu SMP Thu Jan 30 17:42:40 UTC 2014 i686 i686 i386 GNU/Linux
The only reason to run a 32bit Linux kernel is if your CPU does not support x86-64 instruction set.
If it doesn't, it must be ten years old, and therefore it's not worth wasting electricity running some damn miners, BUY the coins.
I was running VMware on my laptop to try to get some kind of Linux miner working whilst waiting on the heavycoinpool Windows miner, and unfortunately my version of VMware workstation does not like 64 bit for some reason, even though my host OS is 64 bit. The laptop is only a year old.