The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1  1  0 2X^2+X X^2  1  1  1  1  1  X  1 X^2+X
 0  1 2X^2+2X+1  2 X+1 2X^2+X 2X^2+X+2  1 2X 2X^2+1 2X+2 2X^2+X+2  1  1  1  0  2 X^2 2X^2+2X+1 X^2+2X+1 2X^2+2X X^2+2X+2  1
 0  0 2X^2  0 X^2 2X^2 X^2 X^2  0 2X^2  0 2X^2 2X^2  0 X^2 2X^2 X^2 X^2 X^2  0 X^2 2X^2 2X^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+426x^43+276x^44+8x^45+552x^46+468x^47+12x^48+426x^49+6x^51+12x^53

The gray image is a linear code over GF(3) with n=207, k=7 and d=129.
This code was found by Heurico 1.16 in 34.6 seconds.