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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+68x^85+130x^86+222x^87+274x^88+380x^89+459x^90+546x^91+605x^92+762x^93+929x^94+1002x^95+1163x^96+1198x^97+1137x^98+1150x^99+1232x^100+948x^101+948x^102+760x^103+519x^104+522x^105+308x^106+280x^107+211x^108+156x^109+139x^110+100x^111+74x^112+52x^113+39x^114+32x^115+16x^116+10x^117+6x^118+4x^119+1x^122+1x^136

The gray image is a linear code over GF(2) with n=392, k=14 and d=170.
This code was found by Heurico 1.16 in 38.1 seconds.