The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+48x^39+144x^40+150x^41+360x^42+336x^43+258x^44+366x^45+2154x^46+384x^47+9334x^48+4008x^49+336x^50+496x^51+474x^52+282x^53+268x^54+168x^55+48x^56+48x^57+6x^58+6x^60+4x^63+2x^66+2x^69

The gray image is a linear code over GF(3) with n=216, k=9 and d=117.
This code was found by Heurico 1.16 in 0.576 seconds.