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

generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 186.

Homogenous weight enumerator: w(x)=1x^0+60x^186+40x^189+162x^190+62x^192+324x^193+20x^195+40x^198+10x^201+8x^204+2x^285

The gray image is a linear code over GF(3) with n=288, k=6 and d=186.
This code was found by Heurico 1.16 in 0.202 seconds.