The generator matrix

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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+118x^74+396x^75+435x^76+508x^77+360x^78+596x^79+388x^80+416x^81+356x^82+284x^83+99x^84+100x^85+24x^86+4x^87+3x^88+2x^94+2x^102+2x^106+2x^108

The gray image is a linear code over GF(2) with n=632, k=12 and d=296.
This code was found by Heurico 1.16 in 0.64 seconds.