The generator matrix

 1  0  1  1  1  1  1  0  1  1  X  1 2X  1  1 2X^2+2X 2X^2+X  1  1  1  1  1  1  1
 0  1  1  2 2X^2+2X+1 2X^2 2X^2+2  1 2X^2+X 2X+1  1 X+2  1 2X^2+1 2X^2+2X+1  1  1  0 2X 2X^2+X+2 2X^2+X+2 2X^2 2X^2+2X+2 2X^2
 0  0 2X  0  0 2X^2+X 2X^2+X 2X 2X^2+2X  X  X  X 2X^2 X^2 2X  X 2X X^2+2X 2X^2  0 2X^2 X^2+X 2X^2+X 2X^2+X
 0  0  0 X^2  0 X^2 2X^2  0 2X^2 X^2  0 2X^2  0 X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0 2X^2  0 X^2
 0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2 2X^2  0 X^2 X^2 X^2 2X^2  0 2X^2 X^2 X^2 2X^2  0 X^2 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+72x^39+102x^40+252x^41+874x^42+198x^43+3264x^44+3008x^45+4686x^46+11838x^47+8456x^48+9168x^49+11718x^50+3840x^51+324x^52+606x^53+420x^54+102x^55+24x^56+76x^57+20x^60

The gray image is a linear code over GF(3) with n=216, k=10 and d=117.
This code was found by Heurico 1.16 in 2.7 seconds.