The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+151x^80+96x^83+153x^84+320x^85+96x^87+134x^88+70x^92+2x^96+1x^164

The gray image is a linear code over GF(2) with n=340, k=10 and d=160.
This code was found by Heurico 1.16 in 0.801 seconds.