The generator matrix

 1  0  0  1  1  1  0 X^3  1  1 X^3 X^2  1  1  1  1 X^3+X X^3+X  1 X^3+X  1  1  1 X^3+X X^2+X  1  1  1 X^3+X^2  1 X^2 X^2+X  1  1 X^3+X  1  1 X^3+X X^3+X^2 X^3  1  1 X^2  1  0  1  1  1  1 X^2+X X^2+X  1  1 X^3+X  0 X^2+X  0 X^3+X^2+X  1  X X^3+X  1 X^2 X^3 X^2  1  1  1  1 X^3+X^2  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0 X^2+1 X^2+1  1 X^3+X^2+X X^3 X^3+X^2+1  1  1 X^3+X^2  1 X^2+X X+1  1 X^2+X  X  1 X^3+X+1 X^3+X^2+X+1 X^2+X+1 X^2  1 X^2+X X^3+X X^3+X^2  1 X^3+X^2+X+1  1  1 X^2 X^2+1 X^3+X X^3+1 X^3  1  1  1 X^3+X^2+1  0 X^2+X X^3+X+1 X^2 X^3+X^2+X X^3+X^2+1 X^3+X X+1  1 X^3+X  X X^2+X+1  1 X^3+X^2  1  1 X^3+X X^3+X^2+X X^2 X^3 X^3+X^2+X  X  1  1 X^3+X+1  0  0 X^3+1  1 X^2  0 X^3+X^2+X  1 X^3+X^2 X^3+X  0  X X^3+X^2+X X^3+1  1 X^3
 0  0  1 X+1 X^3+X+1 X^3 X^3+X^2+X+1  1 X^3+X^2+X X^2+1  1 X^3+X X^3+X^2+1  X X^3+X+1 X^2 X^3+X^2+1  1  X X^3+X^2+X X^2+X+1 X^3+X^2+X X^2+1  1  0 X^3+X^2+1 X^3+X^2  1  1 X^2+X+1 X^2 X+1 X^2+X X^3+X^2+X  1 X+1 X^3+1 X^3+X^2+X+1  0 X^3+X^2+X+1 X^3+X^2  0  1 X^2  1 X^3 X^3+X^2+X+1 X^3+X^2+1 X^2+X X^3+X  1 X^3+X^2+X X^3+X^2 X^3  1 X^3+X^2+X X^2+1  1 X^3+1  1  1 X^3+X^2+1  1 X^3+X^2+X X^3 X^3+X X^2+X+1 X^2+X+1 X^2+1 X^3+X  X X^2  0 X^2 X^3 X^3+X^2+X+1 X^3+X^2+X  0 X^3+X^2  X X^3+1 X^3
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 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 77.

Homogenous weight enumerator: w(x)=1x^0+112x^77+761x^78+832x^79+1466x^80+940x^81+1009x^82+708x^83+815x^84+348x^85+417x^86+276x^87+268x^88+72x^89+82x^90+40x^91+32x^92+8x^94+1x^96+3x^98+1x^100

The gray image is a linear code over GF(2) with n=656, k=13 and d=308.
This code was found by Heurico 1.16 in 5.19 seconds.