The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+60x^82+202x^83+326x^84+418x^85+450x^86+332x^87+421x^88+274x^89+289x^90+266x^91+226x^92+130x^93+146x^94+108x^95+138x^96+100x^97+62x^98+48x^99+42x^100+24x^101+4x^102+4x^103+6x^104+14x^105+5x^106

The gray image is a linear code over GF(2) with n=356, k=12 and d=164.
This code was found by Heurico 1.11 in 0.531 seconds.