The generator matrix

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

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+206x^82+628x^83+904x^84+1260x^85+1604x^86+1828x^87+1952x^88+2144x^89+2390x^90+2344x^91+2629x^92+2392x^93+2278x^94+2228x^95+1829x^96+1788x^97+1304x^98+1096x^99+738x^100+452x^101+378x^102+152x^103+118x^104+60x^105+30x^106+12x^107+21x^108+2x^114

The gray image is a linear code over GF(2) with n=368, k=15 and d=164.
This code was found by Heurico 1.16 in 60.3 seconds.