The generator matrix

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

generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+81x^80+124x^81+138x^82+76x^83+46x^84+16x^85+22x^86+4x^87+4x^93

The gray image is a linear code over GF(2) with n=656, k=9 and d=320.
This code was found by Heurico 1.16 in 0.375 seconds.