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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+18x^68+62x^69+54x^70+60x^71+47x^72+536x^73+550x^74+532x^75+36x^76+38x^77+26x^78+22x^79+20x^80+4x^81+10x^82+24x^83+5x^84+2x^87+1x^140

The gray image is a linear code over GF(2) with n=592, k=11 and d=272.
This code was found by Heurico 1.16 in 0.516 seconds.