The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+26x^88+272x^89+261x^90+532x^91+392x^92+746x^93+463x^94+836x^95+534x^96+722x^97+451x^98+642x^99+331x^100+586x^101+231x^102+310x^103+183x^104+282x^105+100x^106+78x^107+60x^108+68x^109+17x^110+30x^111+7x^112+12x^113+11x^114+4x^115+1x^116+1x^118+1x^120+1x^122

The gray image is a linear code over GF(2) with n=388, k=13 and d=176.
This code was found by Heurico 1.16 in 6.2 seconds.