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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+159x^82+84x^83+213x^84+84x^85+146x^86+32x^87+114x^88+24x^89+55x^90+20x^91+28x^92+24x^94+4x^95+10x^96+4x^97+16x^98+4x^99+1x^104+1x^116

The gray image is a linear code over GF(2) with n=344, k=10 and d=164.
This code was found by Heurico 1.16 in 0.396 seconds.