The generator matrix

 1  0  1  1  1 X^2  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1 X^2  1  1  0  1 X^2+X  1  1 X^2  1  1 X^2+X  1  1  1 X^2  1  1  1  X  X  X  1  X  1  1  1  1  1 X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2+X  1 X^2+X  1  1 X^2+X X^2+X  1  X  1
 0  1  1  0 X+1  1 X^2+X+1  0  1 X^2  1  1  0 X+1  1 X^2 X+1  1  0  1  1  0  1  1 X^2+X X^2+X+1  1 X^2+X  1  1 X+1  1 X^2+1  1  X X^2+X  1 X^2+X+1 X^2+1  1  X X^2+X X^2+X+1  1 X^2+X  X  1  1 X^2  0  0 X^2  X  0  X X^2+X X^2  1 X^2+1  X X^2+X X^2+X X^2 X^2  0 X^2  X  0  X X^2+X  0 X^2+X X^2  1 X^2+1 X^2+X  1  1 X^2  1 X^2+X+1 X^2+1  1  1 X^2+X  1  0
 0  0  X  0  0  0  0  X  X  X  X  X X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X  X  X  0  0 X^2+X X^2  X  X  0  0  0 X^2+X X^2+X X^2+X X^2 X^2  X X^2 X^2+X  X X^2 X^2+X  0 X^2 X^2+X  X X^2 X^2  0 X^2  X  X X^2 X^2+X  0  0 X^2+X X^2+X X^2 X^2+X  X  X X^2 X^2+X X^2  0 X^2+X  0  X X^2+X  X X^2  X X^2  0  X  0  X  0 X^2+X  X X^2  0
 0  0  0  X X^2 X^2+X X^2+X  X X^2 X^2 X^2+X  X X^2  0 X^2 X^2+X  X  X  0  X X^2+X X^2+X X^2  0  X  0  X  0 X^2  X X^2+X  X  0 X^2 X^2+X  0  X X^2+X  0 X^2  0 X^2+X  0 X^2  0  X  X  X X^2 X^2+X X^2+X X^2+X  0  X X^2  0  0 X^2 X^2+X  X X^2+X  X X^2  0 X^2  0 X^2+X X^2  X X^2  X X^2+X X^2+X  0 X^2 X^2  0 X^2+X X^2 X^2+X  X  X  0  0  X  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+40x^82+142x^83+137x^84+78x^85+106x^86+136x^87+97x^88+52x^89+53x^90+50x^91+47x^92+24x^93+17x^94+20x^95+6x^96+4x^97+6x^98+4x^99+2x^101+1x^122+1x^126

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 0.424 seconds.