The generator matrix

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

generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+12x^21+54x^22+12x^24+2x^27

The gray image is a linear code over GF(3) with n=33, k=4 and d=21.
As d=21 is an upper bound for linear (33,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000198 seconds.