The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+16x^15+54x^16+8x^18+2x^24

The gray image is a linear code over GF(3) with n=24, k=4 and d=15.
As d=15 is an upper bound for linear (24,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000164 seconds.