The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+96x^43+168x^44+8x^45+84x^46+252x^47+12x^48+84x^49+6x^51+6x^52+12x^53

The gray image is a linear code over GF(3) with n=207, k=6 and d=129.
This code was found by Heurico 1.16 in 0.0302 seconds.