The generator matrix

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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+416x^76+240x^77+382x^78+112x^79+333x^80+208x^81+236x^82+16x^83+76x^84+14x^86+8x^88+4x^92+1x^108+1x^116

The gray image is a linear code over GF(2) with n=632, k=11 and d=304.
This code was found by Heurico 1.16 in 2.19 seconds.