The generator matrix

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

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+12x^39+54x^40+6x^42+8x^45

The gray image is a linear code over GF(3) with n=180, k=4 and d=117.
This code was found by Heurico 1.16 in 0.00122 seconds.