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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+184x^88+8x^89+274x^90+60x^91+369x^92+112x^93+406x^94+200x^95+442x^96+272x^97+348x^98+192x^99+324x^100+112x^101+289x^102+56x^103+153x^104+8x^105+87x^106+4x^107+92x^108+53x^110+24x^112+15x^114+10x^116+1x^148

The gray image is a linear code over GF(2) with n=388, k=12 and d=176.
This code was found by Heurico 1.16 in 2.69 seconds.