The generator matrix

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

generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+72x^24+8x^27

The gray image is a linear code over GF(3) with n=108, k=4 and d=72.
As d=72 is an upper bound for linear (108,4,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.000288 seconds.