I have followed the docker installation doc for installing it on my machine which is a 32 bit machine running Ubuntu 12.04
The step
$ sudo apt-get in
This is possible these days, with just a simple script. You could use https://gitlab.com/docker-32bit/ubuntu.
Works perfectly on my Ubuntu 16.04 32-bit system. I used it to install the office server Collabora Online for my Nextcloud:
wget https://gitlab.com/docker-32bit/ubuntu/raw/master/build-image.sh
# for Debian, use one of:
# wget https://gitlab.com/docker-32bit/debian/raw/armhf/build-image.sh
# wget https://gitlab.com/docker-32bit/debian/raw/i386/build-image.sh
sudo bash build-image.sh
docker -v
# Docker version 1.13.1, build 092cba3
sudo docker pull collabora/code
sudo docker run -t -d -p 127.0.0.1:9980:9980 -e 'domain=my\\.domain\\.com' --restart always --cap-add MKNOD collabora/code