QECC [[40,14,4]]

This pure code is based on a linear self-orthogonal code over GF(4) with generator matrix:

[1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 a 1 0 0 a a 1 0 1 a a 1 0 1 a a 0 0 1 a 0 0 
0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 a 1 0 0 a a 1 0 1 a a 1 0 1 a a 0 0 1 a 0 
0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 a 1 0 0 a a 1 0 1 a a 1 0 1 a a 0 0 1 a 
0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 a 1 0 0 a a 1 0 1 a a 1 0 1 a a 0 0 1 
a]
[0 0 0 0 1 0 0 0 0 0 0 0 0 a 0 0 0 a a 0 0 1 a a 0 0 1 a a 1 0 1 a 0 1 0 1 0 0 
1]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 a 0 0 a a^2 a 0 a a^2 a^2 a 1 a a^2 a^2 a 0 a a^2 a
0 0 a 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 a 0 0 a a^2 a 0 a a^2 a^2 a 1 a a^2 a^2 a 0 a a^2
a 0 0 a 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 a 0 0 a a^2 a 0 a a^2 a^2 a 1 a a^2 a^2 a 0 a 
a^2 a 0 0 a 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 a 1 0 1 a a 1 0 0 a a 1 0 0 a a 0 0 0 
a]
[0 0 0 0 0 0 0 0 0 1 0 0 0 a 1 0 0 a a 1 0 1 a a 1 0 1 a a 0 0 1 a 0 0 0 1 0 0 
0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 a 1 0 0 a a 1 0 1 a a 1 0 1 a a 0 0 1 a 0 0 0 1 0 
0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 a 1 0 0 a a 1 0 1 a a 1 0 1 a a 0 0 1 a 0 0 0 1 
0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 a 1 0 0 a a 1 0 1 a a 1 0 1 a a 0 0 1 a 0 0 0 
1]

QECC [[40,14,4]]

Matrix with stabilizers/seed generators and circuit for encoding: