The generator matrix

 1  0  0  1  1  1  X X^2  1 X^2+X  1  1  1 X^2  1  1  0  1 X^2+X  0  1  0  1  X  1  1 X^2+X  1  1 X^2+X  1  1  1 X^2+X  1  1  1 X^2  1  1  1  1 X^2+X X^2  0  1  1  1  1 X^2+X X^2+X  1  1 X^2  0 X^2  0 X^2+X  1  1 X^2  0  1  1  1  1  1  X  X X^2+X  0  1  1  1 X^2+X  1  0  0  1  1 X^2  1 X^2+X X^2+X X^2  1
 0  1  0  0 X^2+1 X+1  1 X^2 X^2+X+1  1 X^2 X+1 X^2  1 X^2+X+1  0  1  1  0  1  0  1 X+1  1  1 X^2 X^2 X^2+X X^2+X  X X^2+X X^2+X+1 X+1  1 X^2+X X^2+X+1 X^2  1 X^2+1 X^2+X  1 X^2+1  X  1  1 X^2 X+1 X^2  X  1  1  X  1  1  1  1  X  0 X^2+X+1 X^2+X+1  X  1  1 X^2+X X^2+1 X+1 X^2+X+1  1  X  1  X  1  1 X^2+X+1  1 X+1 X^2+X  0 X^2  0  0  X  1  1  1 X^2+X
 0  0  1  1 X^2+1 X^2 X^2+1  1 X^2+X+1  0 X+1 X^2  0  1 X^2+X+1 X+1  0 X^2  1  1 X^2 X^2  0  1 X^2+1  1  1  X X^2+1  1  0  1 X^2+X X+1  1 X^2+1  X  X  0 X^2+X X^2+X X^2+X+1  1 X^2+X X+1 X^2+X  X X^2+X+1 X^2+X+1 X+1 X^2+X X^2+X+1 X+1 X^2+X+1  X X^2+X  1  1 X+1 X+1  1 X^2+X+1  0 X^2+X+1 X^2+X  1  X  1 X^2+X  0 X^2+X X+1 X^2 X^2  0 X^2+X  1  1 X^2+X X^2+X  1 X+1 X^2+X+1 X^2+1 X^2 X^2+1
 0  0  0  X  X  0  X  X  0  X  0 X^2+X X^2+X X^2 X^2+X X^2+X  X  0  0 X^2+X X^2 X^2  X X^2 X^2 X^2 X^2+X  X  0 X^2 X^2+X X^2+X  0 X^2  X X^2 X^2+X X^2+X X^2 X^2 X^2+X  0 X^2+X  0 X^2+X  X X^2 X^2  X X^2+X  0 X^2  X  0 X^2  X X^2 X^2 X^2  X X^2+X  X X^2+X  0  0  0  X  0 X^2+X  0  X X^2+X  X X^2 X^2+X  X  0 X^2+X  0 X^2  0 X^2+X  0 X^2 X^2+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+190x^81+189x^82+280x^83+208x^84+322x^85+135x^86+164x^87+90x^88+142x^89+39x^90+64x^91+38x^92+46x^93+25x^94+16x^95+21x^96+20x^97+12x^98+16x^99+10x^100+16x^101+4x^103

The gray image is a linear code over GF(2) with n=344, k=11 and d=162.
This code was found by Heurico 1.16 in 1.21 seconds.