The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  X  1  X  0  1 X^2+X  0  1  1 X^2+X  X X^2+X  1  1  0  1  1  1 X^2+X X^2  X  0  1  1  1 X^2+X  1  1  1 X^2+X  1  0 X^2  X  1 X^2+X  1  1 X^2  X  1  1  1  1  1 X^2+X  1  X  1  1  1  1  X X^2+X X^2  1  1  1  1  1 X^2  1 X^2  1  1 X^2  1  0  1  X  1  1 X^2  0 X^2  1  1  1  1  1  1
 0  1  0  0  0  0 X^2  1 X^2+X+1 X+1  1  0 X^2+1  1  1  X  1  1 X^2+X X^2 X^2+X  X X^2+X X+1 X^2+1  1 X^2+X  1  1  1 X^2+X  0  1 X^2+X+1 X^2+X+1 X^2  1 X^2+X X^2+1  1  1  X  1 X^2+X  1  0  1  1 X^2+X  1 X^2+X X+1 X^2+X+1  0 X^2 X+1  1 X^2  X  1  1 X^2+1  0  1  1  1  1  X X^2+X+1 X^2+X+1 X^2+1  1  X  1 X^2+1  1  0 X^2+X X^2+X X^2  1 X^2+X  X  X X^2  1 X^2+X X^2  1 X^2+1 X^2  X
 0  0  1  0  0  1 X+1  1  1 X^2  0  1 X^2+1 X^2+X+1  0  0 X^2  1 X^2+1 X^2+X  1  1  X  X  X X^2+1 X^2+X+1 X+1 X^2+1  0  1  X X^2+1  0 X^2+X X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+1  1 X+1  1  X  0 X^2 X^2+X+1 X^2+1 X^2  1 X^2+X X+1 X^2+X+1 X^2+1  1  X  X  1 X^2  0  1 X^2+X+1 X^2+X  X X^2+X X^2+1  0  X X^2+X  1 X+1  0  X  X X+1  0  X X^2+X X^2+X X^2 X+1 X^2+X  1  1 X^2+1  1  1  1 X^2  1 X^2+X+1
 0  0  0  1  1  1  0 X^2+X+1 X^2+1  X  1 X+1  0 X^2  1 X^2 X^2 X^2  0  1 X^2 X+1  1 X^2+X  1  1 X^2+1 X+1  X X^2+1 X^2  1  X X^2+X X^2+1  0  1 X^2+X X^2+X  1 X+1 X^2+1 X^2+X X^2+1  X X^2+1 X^2 X^2+X+1  X  1  X  1 X^2+X+1 X+1 X^2+X+1 X^2+X X^2  X X+1  1 X^2+X X^2 X^2 X^2+X+1  0 X^2 X^2+X X^2  0 X^2+X X+1  1  0  1 X^2+X+1  0  1 X^2+1  1 X^2+X+1 X^2+X+1  X X^2+X X+1  1  1  X  0 X^2+X+1  1  1  X
 0  0  0  0  X  0  X  0  X  X X^2  X  0 X^2+X  X  0  0  X X^2+X X^2+X X^2  X  0  X X^2  0 X^2  X X^2 X^2+X X^2  0  X  0  X  0 X^2 X^2+X  X  0  X X^2+X X^2  0 X^2 X^2 X^2+X X^2  0  0 X^2+X X^2 X^2+X X^2 X^2+X X^2+X  X X^2+X X^2  X X^2+X X^2  0 X^2+X  0 X^2+X  0  0 X^2  0 X^2+X X^2 X^2+X  0 X^2 X^2 X^2+X X^2 X^2 X^2+X  0 X^2  X X^2+X  0  X X^2+X  X X^2  X X^2 X^2+X
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 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+318x^82+528x^83+1013x^84+1148x^85+1600x^86+1484x^87+2143x^88+2100x^89+2410x^90+2512x^91+2738x^92+2356x^93+2298x^94+2176x^95+2143x^96+1556x^97+1390x^98+868x^99+757x^100+404x^101+362x^102+172x^103+131x^104+48x^105+56x^106+4x^107+28x^108+4x^109+12x^110+6x^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 72.7 seconds.