The generator matrix

 1  0  0  1  1  1 2X  1  1 2X^2+X  1  1  1  1  1  1  1 X^2+2X 2X^2+2X  1  1  1 X^2  1
 0  1  0  1 2X^2+2X  2  1 2X^2+1  2  1 2X+2  0 2X^2+X+1 X+2 X^2 X^2+X 2X^2+2X+2  0  1 X+1 X^2+2X 2X^2+2X+1  1 2X^2+1
 0  0  1  2 2X^2+2X+1  2 2X+1 2X^2+1  X 2X^2+X+2 2X+1 X+2 2X^2+X 2X+1 X^2+X X^2+X+2 X^2+2X  1 2X^2+2X+2 2X^2+2X+2 X^2+2X 2X^2 2X+1 2X^2+X+1
 0  0  0 2X 2X^2+2X X^2 X^2+X 2X^2+X X^2+X  X  X 2X^2+X X^2+2X 2X  X X^2+2X 2X^2 X^2+X  0  X 2X  X 2X 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+318x^40+654x^41+2030x^42+4320x^43+6342x^44+9314x^45+21840x^46+20928x^47+29650x^48+38844x^49+20820x^50+13028x^51+6912x^52+1722x^53+138x^54+156x^55+78x^56+26x^57+24x^58+2x^60

The gray image is a linear code over GF(3) with n=216, k=11 and d=120.
This code was found by Heurico 1.16 in 19.3 seconds.