The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+218x^81+226x^82+298x^83+142x^84+228x^85+164x^86+182x^87+67x^88+128x^89+60x^90+92x^91+45x^92+70x^93+34x^94+30x^95+12x^96+18x^97+8x^98+6x^99+5x^100+10x^101+2x^102+2x^106

The gray image is a linear code over GF(2) with n=344, k=11 and d=162.
This code was found by Heurico 1.11 in 63.3 seconds.