The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3  X X^3  X  0  X  0  X  X  X X^3+X^2  X  X  X  X X^2 X^2  X X^3  X X^2  X  X  0 X^3+X^2 X^3+X^2  X  X  X  0 X^3+X^2  X X^3  X X^2  1  1  1  1  1  1  1  1 X^2 X^2  X X^3 X^2  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^3+X^2+X  0 X^2+X X^2  X X^3+X^2  X X^3 X^3+X^2+X X^3 X^2+X X^3 X^3+X^2+X X^3 X^2+X X^3+X^2 X^3+X X^2 X^3+X X^3+X^2 X^3+X X^2 X^3+X X^2+X  X X^2+X  X X^3+X^2+X  X X^3+X^2+X  X X^3 X^2  X  X  0 X^3+X^2 X^3+X X^3+X  X  X X^2+X  X X^3+X  X X^3+X^2+X X^3+X^2+X  X  X  X  X  X  X  X  X X^2+X  X X^3+X  X  0 X^3+X^2  0 X^3+X^2 X^3 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^2 X^2 X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3 X^3 X^3 X^2 X^3+X^2  0  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^2 X^2  0 X^3  0 X^2 X^3 X^3+X^2 X^2  0 X^3+X^2 X^3 X^2 X^2 X^2  0 X^2 X^2  0 X^3 X^2 X^3+X^2 X^2 X^3 X^2  0 X^3  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3  0 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^2 X^2 X^3+X^2 X^2  0  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+115x^80+80x^81+152x^82+32x^83+104x^84+16x^85+8x^86+3x^96+1x^112

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 0.594 seconds.