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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+122x^66+112x^67+233x^68+276x^69+370x^70+808x^71+447x^72+712x^73+316x^74+288x^75+141x^76+68x^77+92x^78+40x^79+34x^80+18x^82+6x^84+10x^86+1x^88+1x^120

The gray image is a linear code over GF(2) with n=576, k=12 and d=264.
This code was found by Heurico 1.16 in 0.922 seconds.