The generator matrix

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

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+337x^88+574x^89+1027x^90+1276x^91+1610x^92+1712x^93+2153x^94+2082x^95+2544x^96+2126x^97+2409x^98+2370x^99+2435x^100+1920x^101+1953x^102+1474x^103+1460x^104+946x^105+830x^106+562x^107+483x^108+202x^109+102x^110+70x^111+58x^112+38x^113+6x^114+4x^115+2x^117+2x^119

The gray image is a linear code over GF(2) with n=392, k=15 and d=176.
This code was found by Heurico 1.16 in 73.2 seconds.