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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+52x^81+62x^82+62x^83+76x^84+46x^85+51x^86+54x^87+46x^88+24x^89+13x^90+10x^91+4x^92+6x^93+1x^94+2x^95+1x^96+1x^130

The gray image is a linear code over GF(2) with n=340, k=9 and d=162.
This code was found by Heurico 1.16 in 0.456 seconds.