The generator matrix

 1  0  0  1  1  1 X^3  1  1  1 X^3+X X^2+X  1 X^3+X^2+X  1  1  1 X^2  0  1 X^3+X X^3+X X^3+X^2+X  1  1  1  X  1  1 X^3+X^2 X^3 X^2  1 X^3+X  1  1  1  1  1 X^2+X  1  1 X^2+X  1  1  X  1  1  0  1 X^3+X X^3+X  1  1  1  1  1  1  X  1 X^2  1  1 X^2+X  1  1  1  1  1  1 X^2+X  1
 0  1  0  0 X^2+1 X^3+X^2+1  1  X X^2+X+1 X^3+X^2+X+1 X^3  1 X^2  1 X^3+X^2 X^3+1 X^2+X  1  1 X^2+X+1 X^3+X  1  1 X^2+1  X  1 X^3+X^2 X+1 X^2+X  1 X^3  X  X  1 X^3 X^3+X^2 X^2+X+1  X X^3  1 X^3+1 X^3+X+1  0 X^3+X^2+X+1 X^2+1  1 X^2+X X^3+X+1 X^3+X  X  1 X^2+X X^3+1  0  1 X^3+X^2 X^3+X^2+X X+1  1 X^3+X^2+X  1 X^3+X^2+X  1  1 X^3+X+1 X^3+X^2+X X^2 X^3+X^2+X X^3 X^2  1  0
 0  0  1 X+1 X^3+X+1 X^2 X+1 X^3+X  1 X^3  1 X+1 X^3+1 X^3 X^2+X X^3+X^2+X X^3+X^2+1 X^2+1 X^2+X X^2+X+1  1 X^3+X X^3+X^2+1 X^2+1 X+1  X  1  X  0 X^3+X^2+X+1  1  1 X^2+1 X^2 X^3 X+1  1  0 X^3+X^2+X X^3+X^2+X+1 X^3+X^2 X^3+X^2  1 X^3+X^2+X X^3+1 X^3+X+1 X^3+X+1  0  1 X^2+X+1 X^3+X  1 X^3+X+1 X^3+X^2+1 X^3+X  X X^3+X X+1 X^2+1 X^2+X X^3 X^3+1 X^2 X^3+X^2+X X^3+X+1 X^3+X^2  0 X^3+X^2+X+1 X^3+X^2+1 X^3+1 X+1  0
 0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 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+152x^67+509x^68+1148x^69+1034x^70+1282x^71+894x^72+1004x^73+527x^74+516x^75+385x^76+340x^77+161x^78+130x^79+65x^80+36x^81+5x^82+1x^84+1x^86+1x^92

The gray image is a linear code over GF(2) with n=576, k=13 and d=268.
This code was found by Heurico 1.16 in 3.86 seconds.