The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+322x^45+216x^48+72x^51+96x^54+18x^57+4x^63

The gray image is a linear code over GF(3) with n=72, k=6 and d=45.
As d=45 is an upper bound for linear (72,6,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.663 seconds.