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

generates a code of length 93 over Z3[X]/(X^3) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+90x^184+384x^185+10x^186+186x^188+4x^189+24x^191+6x^192+18x^193+4x^198+2x^204

The gray image is a linear code over GF(3) with n=837, k=6 and d=552.
This code was found by Heurico 1.16 in 1.56 seconds.