QECC [[20,4,4]]

This pure code is based on a doubly-even weakly self-dual binary code with generator matrix:

[1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1]
[0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1]
[0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1]
[0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0]
[0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0]
[0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1]

QECC [[20,4,4]]

Binary matrix with stabilizers/seed generators and circuit for encoding: