The generator matrix

 1  0  1  1  1  1  1 2X^2  1  1  1 2X  1  1 2X^2+X  1  1  1  1  1  0  1  1  1
 0  1  1  2  0 2X+1 2X^2+2  1 2X^2+2X 2X^2+2X+2 X+1  1 2X^2+X+2 X^2+2X+1  1 2X^2+1 2X^2  2 X^2+X 2X^2+X+2  1 X^2+X+1 2X^2+2 2X+1
 0  0 2X  0 X^2  X 2X^2+X X^2+X X^2+X 2X^2+2X 2X^2  0 X^2 2X^2+X  X  0 X^2+X 2X 2X^2+2X X^2 X^2+2X 2X^2+X 2X^2+X  X
 0  0  0  X 2X^2+2X 2X^2 X^2+2X 2X 2X^2+2X  X X^2+2X X^2+2X 2X 2X X^2+X 2X^2 2X^2 X^2+2X X^2+2X 2X^2 X^2+2X X^2+X  0 2X^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+180x^40+204x^41+740x^42+1104x^43+2370x^44+2400x^45+7164x^46+7884x^47+10068x^48+13008x^49+7932x^50+3254x^51+1614x^52+528x^53+272x^54+252x^55+36x^56+30x^57+6x^58+2x^60

The gray image is a linear code over GF(3) with n=216, k=10 and d=120.
This code was found by Heurico 1.16 in 2.79 seconds.