The generator matrix

 1  0  0  0  0  1  1  1 X^2+X  1  1  X  0 X^2+X  1  1  1  X  1  1 X^2  0  1  0 X^2+X X^2+X  0  1  1  1  1  1  1 X^2 X^2  1  1  1 X^2  1  1  1  1 X^2+X  0  0 X^2+X X^2  1  0  X  1  1  X  X X^2+X  X  1  1 X^2+X  1  1  X X^2  1  1  1  1 X^2+X  0  1  1  1  1 X^2 X^2+X  1  X  X  X  1 X^2  1  X  1  0 X^2+X  0 X^2  1  0  0
 0  1  0  0  0  X X^2 X^2+X  X X^2 X^2+X  X  X X^2 X^2  X X+1  1 X^2+1 X^2+1  1  1 X^2+1  1  1  1  1 X+1  1 X^2+X+1 X+1 X^2 X^2+X X^2+X  0 X^2+X  0 X^2+X+1  1  X  0 X^2 X^2+1 X^2  1 X^2+X  1  0 X^2+X+1  1  0 X^2+X X^2  1  1  X  1 X+1  X  1 X+1 X^2+X+1  1  1 X^2+1 X+1 X^2+X X+1 X^2 X^2 X^2+1 X+1 X^2 X^2  X X^2 X^2+X  1  1  0 X+1  1  0 X^2  0  0  X X^2+X  1  1  1  1
 0  0  1  0  0  0  0  0 X^2 X^2+1 X+1  1  1  1  1 X^2+X+1  0 X^2+X+1 X^2+1 X^2 X^2 X^2+X X^2+X  X X+1  1 X+1  1  1  1  X X^2  1 X^2+X  1 X^2+X+1  0 X^2  0 X^2+X+1 X^2+X+1 X^2+X X+1 X^2 X+1  1  X  1 X^2+X  1  1  1  X X^2+X+1  X  1 X+1  0 X^2+X+1 X^2+X+1 X^2+X+1 X^2+1  X X^2+X+1 X^2+X  0 X^2  1  X  1 X^2+1  1 X^2+X+1 X+1  1  1  0 X^2+X+1 X^2  1 X^2+1 X^2+1  0  1  0 X^2+X  1 X^2 X^2+X+1  X X^2+X X^2
 0  0  0  1  0  0 X^2+1  1  1  0 X^2+1 X^2+X+1 X^2 X+1  1  X X^2+1 X^2+1  1 X^2+1 X^2+1 X^2+X+1 X^2+X  0 X^2+X X^2+1 X^2+X X^2+X X^2+X+1 X^2 X^2 X+1 X+1  1  X X+1 X^2 X^2+1 X^2+X+1 X^2+1  0 X^2+X X^2+X+1  1  1  0 X+1 X^2+X+1  0  X X+1 X^2+1 X+1 X+1  0 X^2 X^2+X+1  1 X^2+X+1 X^2  1 X^2+X X^2+X X+1 X+1  0 X^2+1 X+1 X^2+X  1 X^2+X+1  0  0 X+1 X+1 X^2+X X^2+X X^2  0  X X^2+X X^2+X+1  X X^2+X+1 X^2  1 X^2  1 X^2 X^2+X+1 X^2+X+1 X^2
 0  0  0  0  1  1  1  X X^2+1 X^2+1  1  X  1 X+1 X^2+X  0 X^2+1  X  1 X^2 X+1 X^2 X^2+1 X^2+X+1 X^2+X+1 X+1 X^2+X X^2+1 X^2  X X^2 X^2+X+1 X^2+X X^2  1  1 X+1 X^2+X+1 X^2+X  0 X^2 X^2 X^2 X+1 X+1 X^2  1 X^2+X X^2+X+1 X+1  1 X^2+X+1 X^2+X+1 X^2+X X^2 X^2+X X^2 X^2+X+1  X X^2  1 X+1 X^2 X+1 X^2+X X+1 X^2  0  1 X+1 X^2+1 X^2+1 X^2 X^2 X^2+X  1 X+1 X+1 X^2 X^2  X  0  1 X^2+X X^2+1 X+1 X^2  0  X X^2+X X+1  1
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 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 81.

Homogenous weight enumerator: w(x)=1x^0+318x^81+777x^82+1130x^83+1811x^84+2078x^85+2848x^86+3138x^87+4171x^88+4334x^89+4669x^90+4878x^91+5259x^92+4970x^93+4921x^94+4212x^95+4184x^96+3336x^97+2629x^98+1938x^99+1496x^100+974x^101+719x^102+322x^103+212x^104+74x^105+76x^106+30x^107+16x^108+10x^109+2x^113+2x^116+1x^130

The gray image is a linear code over GF(2) with n=368, k=16 and d=162.
This code was found by Heurico 1.13 in 81.6 seconds.