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

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+143x^88+387x^90+32x^91+512x^92+92x^93+643x^94+260x^95+716x^96+440x^97+765x^98+444x^99+825x^100+392x^101+684x^102+252x^103+517x^104+88x^105+355x^106+36x^107+218x^108+12x^109+175x^110+99x^112+51x^114+36x^116+10x^118+4x^120+2x^122+1x^148

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 9.78 seconds.