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

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+38x^82+66x^83+119x^84+138x^85+189x^86+254x^87+281x^88+286x^89+313x^90+338x^91+338x^92+344x^93+248x^94+230x^95+188x^96+168x^97+120x^98+76x^99+80x^100+66x^101+47x^102+44x^103+38x^104+18x^105+28x^106+16x^107+7x^108+4x^109+8x^110+4x^112+1x^138

The gray image is a linear code over GF(2) with n=368, k=12 and d=164.
This code was found by Heurico 1.16 in 2.32 seconds.