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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+316x^69+92x^70+436x^71+298x^72+600x^73+784x^74+552x^75+264x^76+348x^77+76x^78+168x^79+10x^80+112x^81+8x^82+24x^83+4x^87+2x^88+1x^128

The gray image is a linear code over GF(2) with n=592, k=12 and d=276.
This code was found by Heurico 1.16 in 49.8 seconds.