The generator matrix

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

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+444x^42+972x^44+1522x^45+1458x^46+3888x^47+2536x^48+2916x^49+3888x^50+1732x^51+286x^54+38x^57+2x^60

The gray image is a linear code over GF(3) with n=216, k=9 and d=126.
This code was found by Heurico 1.16 in 0.364 seconds.