The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X 2X+2  2  1  1  1  1  1  1  1  0  1  X  1  1  X 2X+2  X
 0  X  0  X  0 2X 3X  X 2X+2 3X+2 2X+2 X+2 2X+2  2 X+2 X+2  0  2  X X+2  X 2X+2  X 2X 2X 2X 3X 2X+2 X+2 3X+2 X+2 2X+2  0 3X  2 2X 3X X+2 3X  0 3X+2  0 2X+2 2X 2X+2  X 3X 2X+2 3X 3X+2  X X+2 3X+2  2 3X  2  0  0  0  0 3X 2X+2  2 X+2 2X  0  2 3X+2  2 X+2  X  2
 0  0  X  X  2 X+2 3X+2 2X+2 2X+2 X+2  X  0 2X X+2 3X 2X+2  0 3X  X 2X+2 X+2 2X+2 2X+2  X X+2  2  0 X+2 3X+2 3X  0  0 3X+2 2X 2X 3X 3X+2 3X  2 2X+2  2 X+2 3X+2 3X 2X 3X 3X 2X+2 2X X+2 2X+2 X+2 2X+2 X+2  0  X  X  0  2 2X 3X+2  2  X  0 2X+2 3X+2 3X+2  0  2 3X  2 3X
 0  0  0 2X  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0  0  0  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X 2X  0 2X  0 2X  0  0

generates a code of length 72 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+340x^67+81x^68+472x^69+290x^70+660x^71+538x^72+608x^73+284x^74+404x^75+81x^76+224x^77+2x^78+84x^79+1x^80+8x^81+16x^83+1x^84+1x^124

The gray image is a code over GF(2) with n=576, k=12 and d=268.
This code was found by Heurico 1.16 in 97.5 seconds.