The generator matrix

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

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+1200x^40+2592x^41+5504x^42+10080x^43+23868x^44+26232x^45+59754x^46+76230x^47+81800x^48+104808x^49+77490x^50+35576x^51+18414x^52+6858x^53+780x^54+132x^55+72x^56+34x^57+12x^58+2x^60+2x^63

The gray image is a linear code over GF(3) with n=216, k=12 and d=120.
This code was found by Heurico 1.16 in 157 seconds.