The generator matrix

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

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+38x^88+92x^89+194x^90+324x^91+452x^92+488x^93+501x^94+600x^95+602x^96+610x^97+644x^98+616x^99+598x^100+552x^101+448x^102+442x^103+324x^104+172x^105+154x^106+108x^107+58x^108+36x^109+33x^110+12x^111+30x^112+22x^113+6x^114+8x^115+4x^116+12x^117+2x^118+2x^119+4x^120+1x^128+2x^130

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 7.19 seconds.