The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+122x^81+172x^82+250x^83+118x^84+228x^85+157x^86+206x^87+75x^88+164x^89+115x^90+142x^91+39x^92+90x^93+46x^94+36x^95+18x^96+30x^97+16x^98+4x^99+3x^100+6x^101+4x^102+2x^103+2x^104+1x^110+1x^114

The gray image is a linear code over GF(2) with n=348, k=11 and d=162.
This code was found by Heurico 1.16 in 18.5 seconds.