The generator matrix

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

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+68x^82+432x^83+690x^84+1386x^85+1699x^86+2204x^87+2712x^88+3336x^89+3788x^90+4522x^91+4526x^92+5040x^93+4945x^94+5078x^95+4513x^96+4534x^97+3779x^98+3458x^99+2627x^100+2094x^101+1466x^102+1086x^103+604x^104+378x^105+229x^106+166x^107+62x^108+60x^109+26x^110+12x^111+6x^112+4x^113+2x^115+3x^116

The gray image is a linear code over GF(2) with n=376, k=16 and d=164.
This code was found by Heurico 1.13 in 78.9 seconds.