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

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+82x^82+188x^83+196x^84+152x^85+84x^86+52x^87+38x^88+32x^89+38x^90+28x^91+41x^92+56x^93+20x^94+4x^95+8x^96+1x^100+1x^108+1x^112+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 1.11 in 0.281 seconds.