The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  X  1  1  1  X  1  1 X^2  X  1 X^2  1  X  1  1  1  X  0  1  0  0 X^2  0  1  1  1  0  0  1  1  1  1  X  1  X  1  1  X  1  X  X  1  1  1  0  1  1 X^2  1  X X^2  0  X  1  1
 0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X  X  0  0 X^2 X^2+X X^2+X  X  X  X  X  0  X X^2+X  X  0  X X^2+X X^2 X^2+X X^2 X^2 X^2+X  X  0  0  X X^2  0  X  X  X  X X^2+X  0  X X^2+X X^2  0 X^2 X^2  0  X  X  0  0 X^2+X  0 X^2  0  X  X  X  X X^2  0  0 X^2 X^2 X^2  X  X X^2 X^2  0  X X^2  X  0  X  X X^2+X X^2  0 X^2+X  0  0 X^2  0  X X^2  X X^2+X  0  0 X^2  0 X^2
 0  0  X  0  0  0  0  0  0  0  0  0 X^2 X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2 X^2 X^2+X X^2+X  0  0  X  X  X X^2+X X^2+X X^2+X X^2 X^2 X^2+X  X  X X^2 X^2  X  0  0  0 X^2+X  X  0 X^2 X^2+X  0 X^2 X^2 X^2 X^2+X  X X^2+X  0 X^2+X X^2 X^2+X  0  X  X X^2+X  X X^2  X  X X^2+X X^2+X X^2 X^2 X^2 X^2  0 X^2 X^2  X  0 X^2  X X^2  0 X^2+X X^2+X X^2 X^2+X  X X^2  X  X  0  0 X^2  X X^2  X  X  X  0
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2 X^2+X  X X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  X X^2+X  X X^2  X X^2+X X^2+X  X X^2+X  0 X^2  0  0  0 X^2+X X^2+X  X  0 X^2 X^2+X  X X^2+X X^2  0  X  X X^2 X^2+X  X X^2+X  X  X  X  X  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2+X  X  X  0  0  X X^2+X X^2+X  0  0 X^2+X X^2+X  X X^2+X X^2 X^2  0  X X^2  0  X  X  0 X^2+X  X  X X^2  X  X  0 X^2+X  0  0
 0  0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  X  X  0 X^2  X  0 X^2+X X^2+X  X X^2+X  X X^2 X^2  X X^2 X^2  0 X^2+X X^2  0 X^2+X  X X^2+X X^2  0 X^2+X  X  X X^2  X X^2+X X^2+X  X  0  0 X^2  0  0 X^2+X  X  X  0  0  X  0 X^2  X  X  0 X^2 X^2 X^2 X^2+X  X  0  0  0 X^2  0  X X^2  X  X  X  0 X^2 X^2  0 X^2+X  0 X^2 X^2+X X^2  0 X^2 X^2+X X^2 X^2  0  0 X^2  X X^2  0  X X^2+X
 0  0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X  X  0  X  0 X^2+X X^2+X  0  X X^2 X^2 X^2+X X^2  X X^2+X X^2+X X^2  X X^2 X^2 X^2+X  0  X X^2+X  0  0  0  X X^2+X  0  X  0 X^2+X X^2  X  X  0  0  0 X^2  0 X^2  X  X X^2 X^2+X X^2+X X^2 X^2 X^2  X X^2+X X^2  X X^2+X X^2 X^2+X  X  X  X  X  X  0  X  0  0  X  X X^2 X^2  0  0  X  X X^2+X X^2 X^2  0 X^2 X^2 X^2+X X^2  X  X X^2  0  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+121x^88+8x^89+406x^90+60x^91+504x^92+112x^93+626x^94+264x^95+764x^96+300x^97+816x^98+516x^99+786x^100+356x^101+646x^102+276x^103+487x^104+108x^105+376x^106+32x^107+250x^108+12x^109+142x^110+4x^111+122x^112+48x^114+26x^116+10x^118+8x^120+2x^122+2x^124+1x^144

The gray image is a linear code over GF(2) with n=396, k=13 and d=176.
This code was found by Heurico 1.16 in 10.1 seconds.