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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+102x^86+390x^87+890x^88+1178x^89+1878x^90+2204x^91+2882x^92+3150x^93+4083x^94+3810x^95+4859x^96+4630x^97+5439x^98+4692x^99+5012x^100+4070x^101+4159x^102+3086x^103+2772x^104+1898x^105+1597x^106+966x^107+754x^108+390x^109+278x^110+198x^111+74x^112+38x^113+28x^114+8x^115+4x^116+6x^117+2x^118+4x^119+2x^122+2x^123

The gray image is a linear code over GF(2) with n=392, k=16 and d=172.
This code was found by Heurico 1.13 in 83.8 seconds.