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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1  0  X  1  1  1  1  X  1  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^2+X  0 X^3+X X^3+X^2 X^3+X  0 X^3+X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3 X^2+X X^2 X^3+X X^3 X^3+X^2+X X^3+X^2  X  0 X^2+X X^2  X  0 X^2+X X^3+X^2+X X^2 X^3+X X^3 X^2  X  0 X^3 X^3+X X^3+X X^3+X^2 X^3+X^2 X^2+X X^3+X^2+X X^2+X X^3+X^2+X X^2+X X^3+X^2+X  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X X^3+X X^3  X  X  X X^2+X  0 X^2+X X^3+X^2  X X^2+X  0  0
 0  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0  0  0 X^3 X^3  0
 0  0  0 X^3  0  0  0  0  0  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0  0  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3  0  0  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+17x^68+4x^69+108x^70+128x^71+255x^72+504x^73+236x^74+384x^75+146x^76+4x^77+156x^78+92x^80+12x^82+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 0.484 seconds.