The generator matrix

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

generates a code of length 7 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+14x^12+12x^13+18x^14+26x^15+6x^16+4x^18

The gray image is a linear code over GF(3) with n=21, k=4 and d=12.
As d=12 is an upper bound for linear (21,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000144 seconds.