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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+108x^88+52x^89+276x^90+204x^91+585x^92+404x^93+606x^94+408x^95+685x^96+448x^97+754x^98+496x^99+752x^100+448x^101+520x^102+360x^103+375x^104+172x^105+214x^106+68x^107+99x^108+12x^109+42x^110+58x^112+18x^114+18x^116+3x^120+2x^122+2x^124+2x^128

The gray image is a linear code over GF(2) with n=392, k=13 and d=176.
This code was found by Heurico 1.16 in 7.17 seconds.