The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+64x^87+119x^88+158x^89+432x^90+288x^91+586x^92+390x^93+709x^94+446x^95+792x^96+468x^97+729x^98+432x^99+722x^100+368x^101+526x^102+228x^103+282x^104+102x^105+135x^106+56x^107+23x^108+38x^109+20x^110+14x^111+25x^112+8x^113+5x^114+8x^115+2x^116+4x^117+3x^120+3x^122+3x^124+1x^126+2x^128

The gray image is a linear code over GF(2) with n=388, k=13 and d=174.
This code was found by Heurico 1.16 in 10.7 seconds.