The generator matrix

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

generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+104x^78+264x^79+277x^80+240x^81+381x^82+192x^83+187x^84+240x^85+118x^86+24x^87+12x^88+3x^90+1x^92+2x^98+2x^116

The gray image is a linear code over GF(2) with n=656, k=11 and d=312.
This code was found by Heurico 1.16 in 0.656 seconds.