Tiny Core Linux (http://tinycorelinux.net) is a very small and efficient Linux distribution. But for use with GNS3 on a local Mac or Windows system it's still relative slow, the linux-microcore-6.4 image takes about 25 seconds to boot. The reason is, that the qemu on those systems uses the slow software virtualization.
microcore-mininit is a microcore variant with a stripped down initialization. Additionally the IPv6 kernel modules, iproute2 and nano are added. It boots in about 10s with the slow qemu of Mac / Windows.
But this results in a lower flexibility. For Linux (and GNS3 VM) the normal microcore linux or a docker VM are better alternatives.
The image is downloadable from the GitHub releases area.
If you want to build it yourself, you need a linux system and install packer (https://www.packer.io) and qemu.
Then build the image with
rm -rf output-qemu packer build microcore-mininit.json
As the image should run on the local system, the image can't be installed as an appliance, it has to be installed manually.