The generator matrix

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

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+168x^74+176x^75+592x^76+472x^77+638x^78+384x^79+511x^80+208x^81+414x^82+272x^83+115x^84+24x^85+84x^86+23x^88+6x^90+4x^92+2x^94+1x^108+1x^112

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 0.813 seconds.