The generator matrix

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

generates a code of length 93 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+328x^82+636x^83+1446x^84+1516x^85+2490x^86+2400x^87+3783x^88+3328x^89+5092x^90+4108x^91+5398x^92+4520x^93+5585x^94+4356x^95+4833x^96+3480x^97+3808x^98+2348x^99+2216x^100+1308x^101+1201x^102+456x^103+445x^104+184x^105+154x^106+28x^107+44x^108+25x^110+4x^111+10x^112+2x^114+3x^118

The gray image is a linear code over GF(2) with n=372, k=16 and d=164.
This code was found by Heurico 1.13 in 79.4 seconds.