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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+96x^85+414x^86+878x^87+1421x^88+1816x^89+2224x^90+2646x^91+3412x^92+3588x^93+4372x^94+4374x^95+5031x^96+4846x^97+5106x^98+4574x^99+4615x^100+3864x^101+3274x^102+2484x^103+2181x^104+1516x^105+1100x^106+660x^107+426x^108+280x^109+134x^110+80x^111+56x^112+22x^113+14x^114+16x^115+7x^116+4x^117+2x^118+2x^120

The gray image is a linear code over GF(2) with n=388, k=16 and d=170.
This code was found by Heurico 1.13 in 81.7 seconds.