The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1 X^2  1 X^2+X  1  0  1  1 X^2 X^2  1 X^2+X  1  1  1  0  X  1 X^2+X X^2  0  1  1 X^2 X^2+X X^2+X X^2+X  1  1 X^2+X  1  1 X^2+X  1  1 X^2  1  1  X  1  1  1  1  X  0 X^2  1  1  1 X^2+X  1  1  X X^2+X  0  1  1 X^2  X  1  1 X^2  1  0  1  1  1 X^2+X X^2 X^2+X X^2+X  0  1  1  X  1  1  1  1  X  1  1  0  X  1  1  1  1
 0  1  0  0  0  0  0 X^2 X^2  1  1  1  1  1  1 X+1 X^2+X X^2+X X^2+X  1  1 X^2+X+1 X^2+X X+1  X X+1  1 X^2 X+1  1  0  1  0 X^2  1  1  X  1  1 X^2+1  1 X^2 X^2+1  0 X^2+X+1 X^2+1  1 X^2  0  1 X^2+X  X  0 X^2+X+1  1  0  X  X X+1 X+1  1 X^2+X X^2+1  1  X  1 X^2+X X+1  1  0 X^2+X X^2  1  1  1 X^2  0  1  1 X^2 X^2+X  X  0  1 X^2  0  X  0 X+1 X^2+X+1 X^2+X  X  1  1  1 X^2+X X^2+1  0  0
 0  0  1  0  0 X^2  1 X^2+1  1  0  1 X+1 X^2+X+1 X^2+1  0  X  1 X^2+X X^2+X+1 X^2+X  0 X^2+X X^2  1  1 X^2+1  1  1  0  1  1 X^2+X  0 X^2+X+1 X^2+X+1  1  1 X^2+1 X^2 X^2+X  X X^2  0  1 X+1  1  X  X X^2+1  X X+1 X^2 X^2+X  0 X^2+X X^2+X  1  X  1  X X^2+X X^2+X  1 X^2+X+1 X^2 X^2 X^2+X+1 X^2  0  1  1  1 X^2+X  X  0 X^2+X+1 X^2  X X^2+X+1  1  1  1 X^2+X X^2+X  1  1  X X^2+X X^2  X X^2 X^2+X+1  1 X^2+1  1 X^2+1 X^2+X+1  X  0
 0  0  0  1  0 X^2+1  1  0  1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X  0 X^2+X X+1 X^2+X X^2+X  1 X^2+X  1 X+1 X^2+X+1  1 X^2+1 X^2+X X^2+X X^2 X^2+1 X^2+1  0  0 X^2  1 X^2 X+1  X X^2+X X^2  1 X^2+1 X^2+X+1  1  1 X+1 X^2+1  X X^2+X+1 X^2+X X^2  0  1 X^2+1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^2+1 X^2+1  1 X^2  1  X X^2+1 X^2+X+1 X^2+X X+1  X X^2+1  1  X X^2+X+1 X^2+X+1 X^2+X  0  1 X+1  X  1  X X^2+X X^2+X+1 X^2+X X^2+1 X^2+X+1 X^2+X X^2+X X^2+X+1 X^2+X+1  1 X^2+1  X X+1  0
 0  0  0  0  1  1 X^2  1  1 X^2+1 X^2  1 X+1  0  1  0 X^2+1 X^2+X+1  X  X X^2+X+1 X^2+X X^2+X+1  1 X^2+X+1  X X+1 X^2+X X^2+X+1 X^2+X X^2+X+1 X^2+1 X^2+X X^2  0 X^2+X+1 X^2+X X^2+1 X+1 X+1  0 X^2+X+1 X^2+X  0 X^2+1  0 X^2  0 X^2 X^2+1 X^2 X+1  X  1  X X^2+X X^2+X  1 X^2+1  X  X  0  X X^2+X  1 X^2+1 X^2+X+1 X^2+X+1  X  1 X^2+X+1 X^2+X+1  0  1 X^2+1 X^2+1 X^2+X X^2  1 X^2+X+1 X+1 X^2+X+1  1  0 X^2 X+1 X^2+X  0 X^2+X X^2  1  1  X  0 X^2+X X^2 X+1  1  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+58x^88+356x^89+752x^90+974x^91+1264x^92+1488x^93+1745x^94+2104x^95+2187x^96+2230x^97+2325x^98+2272x^99+2288x^100+2254x^101+2141x^102+1976x^103+1562x^104+1452x^105+1127x^106+708x^107+530x^108+352x^109+296x^110+140x^111+68x^112+58x^113+26x^114+12x^115+10x^116+2x^117+2x^118+4x^119+2x^122+2x^123

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 70.2 seconds.