The generator matrix

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

generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+132x^184+156x^185+56x^186+240x^187+282x^188+74x^189+228x^190+186x^191+22x^192+114x^193+102x^194+40x^195+102x^196+102x^197+16x^198+30x^199+60x^200+8x^201+24x^202+12x^203+6x^204+48x^205+60x^206+6x^207+6x^208+6x^209+4x^210+30x^211+6x^213+6x^214+6x^215+2x^216+6x^217+2x^219+6x^220

The gray image is a linear code over GF(3) with n=288, k=7 and d=184.
This code was found by Heurico 1.13 in 0.231 seconds.