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.