The generator matrix

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

generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 173.

Homogenous weight enumerator: w(x)=1x^0+24x^173+114x^174+168x^176+336x^177+468x^179+486x^180+978x^182+516x^183+1344x^185+694x^186+1728x^188+748x^189+2118x^191+894x^192+1980x^194+866x^195+1854x^197+646x^198+1320x^200+488x^201+822x^203+338x^204+270x^206+134x^207+42x^209+102x^210+6x^212+54x^213+44x^216+28x^219+26x^222+18x^225+14x^228+8x^231+2x^234+4x^237

The gray image is a linear code over GF(3) with n=288, k=9 and d=173.
This code was found by Heurico 1.16 in 23 seconds.