The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+184x^89+316x^90+546x^91+471x^92+696x^93+570x^94+738x^95+593x^96+642x^97+537x^98+566x^99+402x^100+486x^101+263x^102+358x^103+188x^104+208x^105+136x^106+100x^107+56x^108+48x^109+30x^110+24x^111+10x^112+6x^113+3x^114+4x^115+6x^116+2x^117+1x^118+1x^124

The gray image is a linear code over GF(2) with n=388, k=13 and d=178.
This code was found by Heurico 1.16 in 24.7 seconds.