The generator matrix

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

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+274x^81+324x^82+452x^83+240x^84+562x^85+331x^86+330x^87+187x^88+378x^89+195x^90+206x^91+77x^92+154x^93+103x^94+78x^95+28x^96+68x^97+25x^98+22x^99+11x^100+36x^101+14x^102

The gray image is a linear code over GF(2) with n=348, k=12 and d=162.
This code was found by Heurico 1.16 in 17.5 seconds.