The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+137x^86+12x^87+368x^88+52x^89+507x^90+152x^91+660x^92+248x^93+734x^94+380x^95+788x^96+380x^97+815x^98+356x^99+648x^100+276x^101+533x^102+104x^103+395x^104+64x^105+197x^106+20x^107+148x^108+4x^109+104x^110+53x^112+41x^114+8x^116+4x^118+2x^120+1x^136

The gray image is a linear code over GF(2) with n=388, k=13 and d=172.
This code was found by Heurico 1.16 in 9.71 seconds.