The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+77x^86+320x^87+653x^88+996x^89+1277x^90+1366x^91+1657x^92+1920x^93+2227x^94+2502x^95+2355x^96+2428x^97+2402x^98+2484x^99+2242x^100+1818x^101+1621x^102+1208x^103+1021x^104+768x^105+508x^106+362x^107+237x^108+124x^109+67x^110+70x^111+26x^112+8x^113+4x^114+4x^115+2x^117+8x^118+4x^119+1x^122

The gray image is a linear code over GF(2) with n=388, k=15 and d=172.
This code was found by Heurico 1.16 in 69.1 seconds.