The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+994x^42+954x^43+2736x^44+4266x^45+5508x^46+7560x^47+11394x^48+9450x^49+8262x^50+5674x^51+1584x^52+396x^53+224x^54+36x^57+10x^60

The gray image is a linear code over GF(3) with n=216, k=10 and d=126.
This code was found by Heurico 1.16 in 4.04 seconds.