The generator matrix

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

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+304x^82+478x^84+422x^86+302x^88+220x^90+123x^92+74x^94+43x^96+56x^98+10x^100+12x^102+2x^104+1x^108

The gray image is a linear code over GF(2) with n=348, k=11 and d=164.
This code was found by Heurico 1.16 in 0.633 seconds.