tiny-core-linux-64-bit
First download the 64 bit versions of TinyCore bzImage64 19-Jul-2010 18:14 2.4M microcore64.gz 22-Nov-2010 22:39 4.2M
http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/release/distribution_files/
Next you'll have to extract the files from the iso (magicdisc? or ISOBuster?)
Then you replace the original bzImage & core with the 64 bit versions.
You will then boot with the 64 bit kernel, the appbrowser should automatically use the 64 bit extensions.
http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/tcz_3x.html
(NOTE from the command line you can also use "ab" for cli appbrowser)