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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+123x^82+61x^84+96x^85+95x^86+320x^87+34x^88+96x^89+113x^90+31x^92+53x^94+1x^168

The gray image is a linear code over GF(2) with n=348, k=10 and d=164.
This code was found by Heurico 1.16 in 32.3 seconds.