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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+324x^67+80x^68+364x^69+374x^70+404x^71+1153x^72+356x^73+356x^74+268x^75+71x^76+212x^77+6x^78+92x^79+5x^80+28x^81+1x^84+1x^128

The gray image is a linear code over GF(2) with n=576, k=12 and d=268.
This code was found by Heurico 1.16 in 66 seconds.