The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1 X^3+X  1  0  1  1  1  1  1 X^3 X^3+X^2+X  1  1  1  1 X^2 X^3+X  1 X^3+X X^3  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1 X^2+X  1  1 X^3+X^2+X  1  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1  0  1 X^2+1  1 X^3+X^2+X X^3+X+1 X^2 X^3+X^2+1 X^2+X  1  1 X^3+1 X^3+X^2 X^3+X X^2+X  1  1 X^3+X+1  1  1 X^3  1  0  X X^2 X^3+X X^3 X^2 X^3+X  X X^3+X^2 X^2 X^3 X^3+X^2+X X^3+X^2+X X^2+X  X X^2 X^3+X+1  1 X^3+X^2+1 X^2  1 X^3+1  1  X
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^2  0  0 X^3 X^2 X^2 X^3 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0  0  0 X^3 X^3  0 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3+X^2 X^3 X^2
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0  0 X^3 X^3  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 67.

Homogenous weight enumerator: w(x)=1x^0+152x^67+223x^68+478x^69+447x^70+542x^71+477x^72+566x^73+415x^74+420x^75+204x^76+98x^77+17x^78+34x^79+5x^80+2x^81+1x^82+4x^83+4x^85+4x^89+1x^100+1x^104

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 0.594 seconds.