The generator matrix

 1  0  1  1  1 X^2  X  1  1  1 X^2+X  1  1  1 X^2+X  1  1 X^2+X  1  1 X^2  1  1 X^2  1  1 X^2  1  1 X^2  0  1  1  1 X^2+X  1  X  1 X^2  1  1 X^2+X  1 X^2+X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1  1 X^2  1  1  1 X^2  1  1 X^2  1  1
 0  1  1 X^2+X X^2+X+1  1  1 X+1  X X^2+1  1 X^2  X X+1  1  X X+1  1  0  1  1  0  1  1  0 X^2+X+1  1 X^2+X  1  1  1 X^2 X^2+X+1  X  1  1  1  0  1  0  X  1  X  1 X^2+X+1 X^2+1 X^2+X+1  1 X^2+X X+1 X^2+1 X^2+X+1  1 X+1 X^2+1 X+1 X^2+1 X+1 X+1  1 X^2+1 X^2+X+1 X^2+1 X+1  1  0 X^2 X^2  0 X^2+X  X X^2 X^2  0 X^2+X  0 X^2  X X^2+X X^2+X  X  X X^2+X  X X^2 X^2
 0  0  X  0 X^2+X  X  X X^2  X X^2  0  X X^2+X X^2  0  0  X X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0  X  X  0  X X^2+X  0 X^2+X X^2 X^2+X  0 X^2  X  0  0  X  0 X^2+X  X  0 X^2 X^2  X  X X^2 X^2+X X^2+X X^2+X  X  0 X^2  0 X^2 X^2+X  X X^2+X X^2+X X^2  0 X^2  0 X^2 X^2  X X^2+X  0 X^2  0 X^2  X X^2+X X^2  X  0  X X^2+X  X  0 X^2 X^2 X^2+X  X
 0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 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+64x^81+112x^82+100x^83+140x^84+104x^85+76x^86+104x^87+108x^88+68x^89+28x^90+52x^91+4x^92+16x^93+36x^94+2x^96+4x^97+4x^114+1x^128

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 0.523 seconds.