The generator matrix

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

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+206x^82+188x^83+317x^84+196x^85+252x^86+120x^87+173x^88+100x^89+90x^90+96x^91+96x^92+20x^93+60x^94+32x^95+26x^96+4x^97+30x^98+12x^99+22x^100+4x^104+2x^106+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 0.604 seconds.