The generator matrix

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

generates a code of length 20 over Z3[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+120x^39+54x^40+64x^42+2x^45+2x^51

The gray image is a linear code over GF(3) with n=180, k=5 and d=117.
As d=119 is an upper bound for linear (180,5,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.00457 seconds.