The generator matrix

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

generates a code of length 99 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+116x^88+370x^89+694x^90+908x^91+1283x^92+1400x^93+1837x^94+1826x^95+2126x^96+2082x^97+2680x^98+2340x^99+2634x^100+2156x^101+2447x^102+1776x^103+1610x^104+1220x^105+1100x^106+672x^107+521x^108+402x^109+221x^110+146x^111+75x^112+40x^113+38x^114+8x^115+16x^116+10x^117+7x^118+4x^119+2x^124

The gray image is a linear code over GF(2) with n=396, k=15 and d=176.
This code was found by Heurico 1.16 in 71 seconds.