The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+134x^85+135x^86+202x^87+108x^88+124x^89+40x^90+62x^91+25x^92+18x^93+47x^94+50x^95+24x^96+36x^97+6x^99+8x^101+2x^106+1x^112+1x^116

The gray image is a linear code over GF(2) with n=356, k=10 and d=170.
This code was found by Heurico 1.16 in 0.446 seconds.