The generator matrix

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

generates a code of length 21 over Z3[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+144x^41+18x^42+72x^44+2x^45+6x^48

The gray image is a linear code over GF(3) with n=189, k=5 and d=123.
This code was found by Heurico 1.16 in 0.00218 seconds.