QECC [[15,3,5]]

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

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

QECC [[15,3,5]]

Matrix with stabilizers/seed generators and circuit for encoding: