The generator matrix

 1  0  1  1  1 X^2  X  1  1  1 X^2+X  1  1  1 X^2+X  1  1 X^2+X  1  1 X^2  1  1 X^2  1  1 X^2  1  1 X^2  0  1  1  1 X^2+X  1  X  1 X^2  1  1 X^2+X  1 X^2+X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1
 0  1  1 X^2+X X^2+X+1  1  1 X+1  X X^2+1  1 X^2  X X+1  1  X X+1  1  0  1  1  0  1  1  0 X^2+X+1  1 X^2+X  1  1  1 X^2 X^2+X+1  X  1  1  1  0  1  0  X  1  X  1 X^2+X+1 X^2+1 X^2+X+1  1 X^2+X X+1 X^2+1 X^2+X+1  1 X+1 X^2+1 X+1 X^2+1 X+1 X+1  1 X^2+1 X^2+X+1 X^2+1 X^2+X+1  1  0 X^2 X^2  0  X X^2 X^2+X  X  X  0 X^2+X  1 X+1  1 X^2+1  0  1 X+1 X^2+X+1  1 X^2 X^2
 0  0  X  0 X^2+X  X  X X^2  X X^2  0  X X^2+X X^2  0  0  X X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0  X  X  0  X X^2+X  0 X^2+X X^2 X^2+X  0 X^2  X  0  0  X  0 X^2+X  X  0 X^2 X^2  X  X X^2 X^2+X X^2+X X^2+X  X  0 X^2  0 X^2 X^2+X  X X^2+X X^2+X X^2  0 X^2  0 X^2 X^2  X X^2+X  X  0 X^2  0 X^2+X X^2  X X^2+X  X  0 X^2+X  X X^2  X  0 X^2+X X^2  X
 0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2
 0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 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+69x^82+88x^83+141x^84+72x^85+138x^86+100x^87+143x^88+40x^89+57x^90+56x^91+52x^92+16x^93+24x^94+12x^95+9x^96+5x^112+1x^132

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 0.544 seconds.