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

generates a code of length 99 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+90x^86+160x^87+171x^88+248x^89+363x^90+470x^91+573x^92+600x^93+742x^94+998x^95+1052x^96+972x^97+1188x^98+1332x^99+1210x^100+1106x^101+1049x^102+940x^103+665x^104+506x^105+382x^106+388x^107+289x^108+198x^109+181x^110+164x^111+111x^112+74x^113+74x^114+26x^115+16x^116+8x^117+25x^118+2x^119+8x^120+1x^126+1x^138

The gray image is a linear code over GF(2) with n=396, k=14 and d=172.
This code was found by Heurico 1.16 in 38.3 seconds.