Tinycore linux is a distribution of small size linux. It core is as small as 16M.
Core is the base system which provides only a command line interface and is therefore recommended for experienced users only. Command line tools are provided so that extensions can be added to create a system with a graphical desktop environment. Ideal for servers, appliances, and custom desktops.
Base Core, the image of docker is only 8.7M.
docker pull tatsushid/tinycore
This time I will write about running docker in Tinycore.
You can find link here
http://forum.tinycorelinux.net/index.php?topic=21839.0
And some useful page