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

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+152x^88+20x^89+296x^90+60x^91+369x^92+104x^93+388x^94+212x^95+499x^96+256x^97+392x^98+172x^99+292x^100+120x^101+196x^102+60x^103+184x^104+12x^105+116x^106+8x^107+73x^108+72x^110+20x^112+12x^114+9x^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 2.66 seconds.