The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1 X^2+X  1 X^2+X  1  1  0  1  1  1  0  1  0 X^2  1  1  1  X  1  1  1  1  1 X^2+X  1  0  X  1  1  1  1  0  0  1  1  1 X^2+X  1  1  0 X^2 X^2+X  1  1  1  X  0  1 X^2+X  1  1  1  0  X  1  0  1  1  X  1  1  1 X^2+X  1  1  X  1 X^2  1 X^2+X  1  X X^2  1  X  1 X^2  0  0  X  1  1  1  0  1
 0  1  1  0 X^2+X+1  1  X X+1  1 X^2+1  1 X^2+X  0 X^2+X+1  1 X^2+X+1  1 X^2  1  1 X^2+X  1 X^2+X  1 X^2  1  1  1 X^2+X X+1  1  1  0  X X^2+X+1 X^2+1  1  0  1  1 X^2+X+1  1 X^2+X X^2  1  1  1 X+1 X^2+X  1 X^2+X+1 X^2+X+1  1  1  1 X+1 X+1  0  1  1 X^2  1 X^2 X^2+X X^2+X+1  1  1  0  1  X X^2  1 X^2+X+1 X^2+X+1 X^2  1 X^2+X+1 X^2+X+1  1  X  1 X^2+1  1 X+1  1  1 X+1  X X+1  1 X^2  X  1  1 X^2 X^2  X  0
 0  0  X  0 X^2+X  0  0  X  0 X^2+X  0  0  X X^2 X^2+X  0 X^2+X  X X^2 X^2+X  X  0 X^2+X X^2+X  X X^2+X X^2 X^2+X X^2+X X^2 X^2  0  X  0 X^2+X X^2+X X^2  0 X^2  X  X  0  0 X^2+X  X X^2  0  0  X  0  X  0  X X^2+X  X  X X^2+X X^2 X^2  0 X^2+X X^2  X  0  X X^2+X  X X^2+X X^2 X^2+X X^2 X^2+X X^2  0  0 X^2+X X^2  X  0  X  X X^2 X^2+X  X X^2+X X^2+X  0  X X^2+X  X  X X^2 X^2+X X^2  X  X  X  0
 0  0  0  X  0  0  X  X  X  X X^2+X X^2  X X^2+X X^2+X X^2  0  0 X^2+X  X  X X^2 X^2  0  0  X X^2  0  X X^2+X X^2+X X^2+X  0 X^2+X X^2+X X^2  0 X^2  X  0 X^2  0 X^2 X^2+X  0  X X^2+X X^2+X X^2+X  X X^2  0 X^2+X X^2+X  0  0  X X^2+X  X X^2  0 X^2 X^2  0  X X^2+X  0 X^2+X  X  0  X  X  0 X^2  0 X^2  0 X^2+X X^2  0 X^2 X^2  0 X^2 X^2  0  X  X X^2 X^2  0 X^2+X  0 X^2+X X^2  X  X  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  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+40x^86+102x^87+185x^88+362x^89+472x^90+544x^91+662x^92+752x^93+947x^94+1126x^95+1130x^96+1316x^97+1274x^98+1172x^99+1333x^100+1030x^101+931x^102+860x^103+603x^104+508x^105+330x^106+228x^107+127x^108+94x^109+66x^110+48x^111+37x^112+30x^113+26x^114+14x^115+12x^116+4x^117+7x^118+4x^120+2x^122+2x^123+1x^124+1x^126+1x^132

The gray image is a linear code over GF(2) with n=392, k=14 and d=172.
This code was found by Heurico 1.16 in 25.4 seconds.