The generator matrix

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

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+180x^184+312x^185+36x^186+168x^187+228x^188+56x^189+216x^190+76x^192+84x^193+168x^194+30x^195+108x^196+48x^197+22x^198+84x^199+8x^201+60x^202+168x^203+2x^204+48x^205+48x^206+2x^207+24x^208+6x^210+4x^222

The gray image is a linear code over GF(3) with n=288, k=7 and d=184.
This code was found by Heurico 1.16 in 70 seconds.