The generator matrix

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

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+136x^81+137x^82+156x^83+129x^84+102x^85+79x^86+104x^87+43x^88+22x^89+33x^90+14x^91+9x^92+8x^93+5x^94+14x^95+9x^96+12x^97+2x^98+8x^101+1x^104

The gray image is a linear code over GF(2) with n=340, k=10 and d=162.
This code was found by Heurico 1.16 in 0.404 seconds.