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  0  1  X  1  X  1  1  1  1  1  1  1  1  1  1  1  0  1  1  X  1  1  1  1  0  1  1  0  1  X  1 X^2  0  1 X^2  1  0  1  1  1  0  1  X  X  1 X^2  0  1  0  1  1  0 X^2 X^2  1  X
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2 X^2  0  X X^2+X  0  0 X^2+X X^2+X X^2 X^2+X  X X^2 X^2  X  X  0 X^2+X  0 X^2  X X^2  0  X  X X^2 X^2  0  X X^2+X X^2+X X^2+X  0 X^2+X  0 X^2 X^2  X  X  0  0  X X^2  X X^2 X^2 X^2+X X^2+X  0 X^2  X X^2  X  X  X  X  X  X  0  0 X^2  X  X  X X^2+X  X  0  X  0  X X^2+X X^2+X  X  X  X  0  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2 X^2+X  X  0  X X^2 X^2+X  0 X^2  X X^2  X X^2  0  X X^2+X X^2 X^2+X  0  X  X  0  X  0  X X^2+X  X  X X^2+X  X X^2+X X^2+X X^2  0  X  0  0 X^2  0 X^2+X  0 X^2+X  X X^2 X^2 X^2+X  X  0  0  X  X X^2+X X^2+X X^2+X X^2  0 X^2+X  0 X^2+X X^2  X X^2  0  X  X  X  X  X X^2 X^2 X^2  X X^2+X X^2 X^2  X  X  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 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+84x^82+12x^83+194x^84+56x^85+272x^86+56x^87+363x^88+176x^89+473x^90+232x^91+501x^92+192x^93+420x^94+160x^95+279x^96+80x^97+147x^98+44x^99+123x^100+8x^101+78x^102+8x^103+61x^104+53x^106+12x^108+6x^110+3x^114+1x^116+1x^140

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 2.48 seconds.