The generator matrix

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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+177x^82+4x^83+239x^84+44x^85+320x^86+148x^87+417x^88+184x^89+485x^90+292x^91+459x^92+176x^93+360x^94+108x^95+187x^96+40x^97+153x^98+24x^99+101x^100+4x^101+78x^102+57x^104+25x^106+9x^108+2x^110+1x^112+1x^144

The gray image is a linear code over GF(2) with n=364, k=12 and d=164.
This code was found by Heurico 1.16 in 2.97 seconds.