The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+432x^47+72x^48+216x^50+8x^54

The gray image is a linear code over GF(3) with n=216, k=6 and d=141.
As d=142 is an upper bound for linear (216,6,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.00216 seconds.