The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+36x^29+22x^30+18x^32+2x^36+2x^39

The gray image is a linear code over GF(3) with n=45, k=4 and d=29.
As d=29 is an upper bound for linear (45,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.13 in 0.000582 seconds.