The generator matrix

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

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+114x^89+423x^90+380x^91+730x^92+488x^93+891x^94+448x^95+778x^96+464x^97+639x^98+354x^99+557x^100+320x^101+471x^102+226x^103+314x^104+142x^105+186x^106+74x^107+72x^108+32x^109+38x^110+22x^111+11x^112+8x^113+4x^114+1x^116+4x^118

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 5.57 seconds.