The generator matrix

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

generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+100x^42+124x^45+12x^48+4x^54+2x^60

The gray image is a linear code over GF(3) with n=66, k=5 and d=42.
As d=42 is an upper bound for linear (66,5,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.00161 seconds.