The generator matrix

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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+148x^75+650x^76+728x^77+664x^78+436x^79+446x^80+228x^81+220x^82+192x^83+156x^84+84x^85+68x^86+40x^87+31x^88+4x^92

The gray image is a linear code over GF(2) with n=632, k=12 and d=300.
This code was found by Heurico 1.16 in 0.375 seconds.