The generator matrix

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

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+44x^81+115x^82+132x^83+143x^84+116x^85+70x^86+98x^87+80x^88+64x^89+38x^90+16x^91+43x^92+28x^93+9x^94+6x^95+4x^96+2x^97+4x^98+4x^99+3x^102+2x^105+1x^112+1x^114

The gray image is a linear code over GF(2) with n=344, k=10 and d=162.
This code was found by Heurico 1.16 in 0.407 seconds.