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  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^3  1  1  1  1  1  1  1  1  0  X  0 X^3  1 X^2  X  1  1
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^2+X X^3+X^2  X X^2 X^3+X X^2 X^2+X  0 X^3+X^2+X X^2 X^3+X^2+X X^3 X^2+X X^3  X  0  X  0  X X^3+X X^3+X^2  X X^2 X^2 X^2+X X^2+X X^3+X^2 X^2 X^3+X  X X^3+X^2 X^3+X X^3+X^2 X^2  X X^3+X X^3+X^2 X^2+X X^3+X^2 X^2+X X^3+X^2+X  0  0  X X^3+X X^3  0 X^3 X^2+X X^3+X^2+X X^2+X X^3+X^2+X X^3 X^3 X^2  0 X^2  0 X^3  0 X^3  X X^3+X^2+X  X  X X^3+X^2+X  X  X X^2+X X^3
 0  0 X^3+X^2  0  0 X^3+X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^3 X^3+X^2  0 X^2 X^3  0 X^3+X^2 X^2 X^2  0 X^3 X^3 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3 X^2  0 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2  0  0  0 X^3 X^3+X^2 X^3  0 X^3 X^2 X^3 X^2 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^3  0  0 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2  0
 0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^2 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3  0 X^3 X^3 X^2 X^3  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2 X^2 X^3+X^2 X^2 X^2  0 X^3 X^3+X^2 X^3 X^3 X^3 X^3  0  0 X^3 X^2 X^2 X^3+X^2  0  0 X^3  0 X^2 X^3+X^2  0 X^3 X^2 X^3 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+40x^74+72x^75+226x^76+272x^77+324x^78+408x^79+151x^80+248x^81+60x^82+96x^83+76x^84+56x^85+16x^86+1x^88+1x^144

The gray image is a linear code over GF(2) with n=632, k=11 and d=296.
This code was found by Heurico 1.16 in 0.61 seconds.