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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+27x^78+44x^79+68x^80+90x^81+78x^82+80x^83+50x^84+36x^85+19x^86+4x^87+9x^88+2x^89+3x^90+1x^154

The gray image is a linear code over GF(2) with n=328, k=9 and d=156.
This code was found by Heurico 1.16 in 0.304 seconds.