The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+66x^40+252x^42+342x^43+810x^44+778x^45+2742x^46+3240x^47+1476x^48+4938x^49+3240x^50+1040x^51+612x^52+72x^54+48x^55+20x^60+4x^63+2x^69

The gray image is a linear code over GF(3) with n=216, k=9 and d=120.
This code was found by Heurico 1.16 in 27.9 seconds.