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 X^2  X  1 X^3  1  1  1 X^2+X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1 X^3+X^2+X  1  1  1 X^3+X^2+X  1 X^2  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  1  1 X^2+X  1 X^3+X+1 X^3  1  1  0  X X^2 X^3+X X^3 X^2 X^3+X  X X^3+X^2 X^3  0 X^3+X^2 X^2+X X^2+X X^3+X  X X^3 X^3+X^2  1 X^3+X X^2+X+1 X^3+X^2  1  X  1 X^2+1
 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^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0  0  0 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^2  0 X^3+X^2 X^2  0 X^3
 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 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0
 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  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  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 69.

Homogenous weight enumerator: w(x)=1x^0+148x^69+198x^70+512x^71+516x^72+440x^73+575x^74+482x^75+397x^76+440x^77+194x^78+114x^79+25x^80+28x^81+8x^82+4x^83+2x^84+6x^87+2x^88+2x^91+1x^106+1x^108

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 0.641 seconds.