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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+110x^83+143x^84+220x^85+102x^86+136x^87+42x^88+36x^89+34x^90+54x^91+28x^92+56x^93+14x^94+16x^95+16x^96+8x^97+4x^99+1x^104+1x^108+1x^110+1x^118

The gray image is a linear code over GF(2) with n=348, k=10 and d=166.
This code was found by Heurico 1.11 in 0.297 seconds.