The generator matrix

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

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+24x^31+36x^32+4x^33+12x^34+4x^39

The gray image is a linear code over GF(3) with n=48, k=4 and d=31.
As d=31 is an upper bound for linear (48,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00046 seconds.