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  X  1  1  X X^2  1  1  1  1  1  1  X  1 X^2+X  1  1  X X^2  1  1  0 X^2+X X^2 X^2  X  0  1  1  1  1  1  1  X X^2  1  1 X^2 X^2+X X^2+X  1  1  1  1 X^2  1  X  1  X  1  1  1  X  1  1  0  1  1  0  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  1  0 X+1  1  1 X^2+1 X^2+1  X  1 X+1 X^2  1 X^2+X+1  1 X^2+1 X^2+X+1  1  0 X^2+1 X^2+X+1  1  1  1  1  1  1 X^2 X^2+X X^2+1 X^2+1  0 X^2+X+1 X^2  0  X  X  1  1 X^2 X^2+X  1 X+1  1  1  0  1  0  1  1 X^2+1  X  1 X^2+X+1  X  1 X^2+X+1  0  1  0
 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^2+1 X^2+X+1 X^2+X+1  1 X^2+X+1 X^2+X X^2+X  1 X^2+1 X^2+1  1  X X^2+X X^2  0 X^2+1 X^2 X^2+X X^2  1 X^2+X+1 X^2+X+1  0  X X^2+X X^2+X+1 X+1 X^2+X  1  X X^2+X  1  1 X^2+X X^2+X X+1 X^2+X  1 X^2+X+1 X^2 X^2+X  1 X^2+X X+1  1  X X^2 X^2+X  1 X^2+1  X X^2+1 X^2  X X^2+X X^2+X X^2+1  0
 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+1  0  0 X+1  X X+1 X^2 X^2+1  1  1 X+1 X^2 X^2+1 X^2+X X^2+X  0 X^2+1  1  X X^2+X+1 X^2+1 X^2 X^2  X X^2+1 X+1  1 X^2+1 X^2+X+1 X^2  0 X^2 X+1  0 X^2+X+1  1  X X+1  X X+1 X^2+X+1 X^2+1  X X+1 X^2+X  X X^2+X+1  1  X X^2 X^2+X X^2+X  X  1 X+1 X+1  1 X^2+X+1  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 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2  0 X^2 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 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0  0
 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 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 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 X^2  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+105x^88+364x^89+555x^90+1086x^91+1068x^92+1852x^93+1504x^94+2156x^95+1817x^96+2520x^97+2101x^98+2756x^99+2141x^100+2518x^101+2093x^102+2124x^103+1380x^104+1446x^105+816x^106+932x^107+453x^108+460x^109+193x^110+150x^111+69x^112+44x^113+20x^114+10x^115+6x^116+10x^117+14x^118+2x^119+2x^121

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 71.5 seconds.