The generator matrix

 1  0  0  1  1  1  0  X  1  1  1  1  0  0 X^2  X  X  1  1  1  1  X  1 X^2+X  1 X^2+X  1 X^2  1 X^2+X  1  1  X X^2  1  1  1  1  1  1  0 X^2+X  1  1  X  1  0  1  1  1  1 X^2  1 X^2 X^2+X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  X  1  1  1  1  1  1  1  1  1
 0  1  0  0  1  1  1 X^2 X^2 X^2 X^2+1 X^2+1  1  1  X X^2+X  1  X  1  1 X^2+1  1 X^2+X  1 X^2+1  1  X  X X^2+X  0  1 X^2+1  X  0 X+1 X+1 X^2+X+1 X^2+X+1  0 X^2  1  1 X+1 X^2+X  1  X  1 X^2+1 X+1 X^2 X^2+X  1  X  1  1  0  1 X+1 X^2+X+1 X+1 X+1 X+1 X^2+X+1  1  1  1 X+1 X^2+X+1  0 X^2+X+1  X X^2+X X^2  0 X^2+X X^2 X^2+X  0 X^2+X+1  X X+1 X^2+X+1  0 X^2  0
 0  0  1  1 X^2 X^2+1  1  1  X X+1 X^2+X X^2+X+1  X X^2+X+1  1  1  1  X X^2+X+1  X  1 X+1 X^2  X  0 X^2 X+1  1 X^2+1  1 X^2+X X^2  1  1 X+1 X^2+X+1  1  1  0 X+1  1  X  X  1 X^2+X+1 X^2+X X^2  0  0  1 X^2+X+1 X^2+X+1  0 X^2+X X^2+1  X X^2  X  0 X^2+X X^2 X^2+X X^2  X  0 X^2+X  0  X X^2+X  X X^2+1 X^2+X X^2+X X+1  1  1  1 X^2+X  0  1  1 X^2+1  1  0 X+1
 0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  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+122x^81+137x^82+206x^83+109x^84+120x^85+33x^86+68x^87+36x^88+50x^89+36x^90+30x^91+28x^92+36x^93+1x^96+8x^97+1x^106+1x^108+1x^118

The gray image is a linear code over GF(2) with n=340, k=10 and d=162.
This code was found by Heurico 1.11 in 0.328 seconds.