The generator matrix

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

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+144x^85+118x^86+188x^87+117x^88+124x^89+59x^90+70x^91+23x^92+32x^93+35x^94+38x^95+26x^96+20x^97+2x^98+2x^99+1x^100+16x^101+6x^103+1x^110+1x^114

The gray image is a linear code over GF(2) with n=356, k=10 and d=170.
This code was found by Heurico 1.11 in 0.328 seconds.