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

generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+398x^79+231x^80+454x^81+89x^82+336x^83+156x^84+256x^85+19x^86+74x^87+12x^88+6x^89+2x^90+4x^91+4x^93+4x^95+1x^114+1x^118

The gray image is a linear code over GF(2) with n=656, k=11 and d=316.
This code was found by Heurico 1.16 in 85.1 seconds.