The generator matrix

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

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+122x^77+355x^78+474x^79+437x^80+474x^81+493x^82+440x^83+431x^84+370x^85+283x^86+124x^87+41x^88+42x^89+2x^90+1x^92+2x^102+2x^103+1x^112+1x^122

The gray image is a linear code over GF(2) with n=656, k=12 and d=308.
This code was found by Heurico 1.16 in 0.703 seconds.