The generator matrix

 1  0  0  0  1  1  1  X  1  X  1  1  1  X X^2  1  0 X^2+X  1  1 X^2+X X^2 X^2  1  1  0  X  1  1  1  0  1  1  1  X  0  1 X^2+X X^2+X  0  1  1  1  X  1 X^2  1  0  X  1 X^2 X^2  1  1 X^2+X  1  1  1  1  X X^2 X^2+X  X  1  1 X^2  1  1  1 X^2  0  0  1 X^2+X  1  1  1  1  X  1  1  1 X^2+X  1  0  1  0  1  X  1  1 X^2+X
 0  1  0  0  X  0  X  X X^2+X+1  1 X^2+X+1  1 X^2+X+1  1  1 X^2+X  0  1  1 X^2+1  1 X^2+X  1  X X^2  1  0 X^2+1  1  X X^2  1  0 X^2+X  0  1  1 X^2  1  1 X^2  1 X^2+X+1  X X^2+X  1 X^2+X+1  1  1 X+1  1  1  0  0  1  0 X^2+X+1  0  1 X^2+X  1 X^2  1 X^2+X+1 X^2+1  1 X^2 X^2  X X^2 X^2+X  X  X  1  0 X^2+1  1 X^2  1  1 X^2+X+1 X^2+1  1 X^2  1 X^2  X X^2+1  1  1 X+1  1
 0  0  1  0  X  1 X+1  1 X^2+X+1 X+1  X X^2+1 X^2  0 X+1  1  1 X^2+X X^2+1 X^2  1 X^2  1 X+1 X^2  X  1  0 X^2+1  0  1 X^2+X+1  0 X^2+X+1  0 X^2+1 X^2+X  X X^2  X  0  0 X+1  1  1  1 X^2+X X^2+1  1 X^2 X^2+X+1 X^2+X X+1 X^2+X+1  1 X^2+X X+1 X^2+X+1  0  1 X^2+X  X X^2+X+1 X+1 X^2+X  0  X X^2+X  0  1  1  1 X^2  X X^2+X X^2+X  X  1  0 X^2+X+1 X+1  0  X  X X^2+X X+1  1  X X^2+X  0 X^2+X+1 X^2
 0  0  0  1 X+1  1  X X+1 X^2+1 X^2+X X^2+1  0  X X+1  1 X^2+X+1  X  1  X  X X^2+1  1 X^2  0 X+1 X^2  0 X+1 X+1  X X+1 X^2+1 X^2+1 X^2+1  1 X^2+1  1  1 X^2+X  0  X  0 X^2+X X+1  X X^2+X+1  X  X X^2+X X^2+X+1 X^2+X+1 X+1  X  0 X^2+1 X^2+X X+1 X^2  0  1 X^2+X+1  1  0 X^2+1  0  0 X^2+X+1 X^2+1 X^2  0  1 X^2  0 X^2 X^2 X^2+X+1  0 X+1 X+1 X^2+1  X X^2+X+1 X^2 X^2+1  X X^2  0 X^2+X X^2+X+1 X^2+X+1 X^2+X+1  X
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  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 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  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+464x^82+256x^83+1328x^84+564x^85+2283x^86+912x^87+2958x^88+1064x^89+3517x^90+1288x^91+3844x^92+1300x^93+3426x^94+1224x^95+2773x^96+844x^97+2172x^98+440x^99+1036x^100+168x^101+487x^102+104x^103+186x^104+28x^105+53x^106+32x^108+12x^110+2x^112+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 84.7 seconds.