The generator matrix

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

generates a code of length 20 over Z3[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+30x^38+10x^39+162x^40+18x^41+12x^42+2x^45+6x^47+2x^48

The gray image is a linear code over GF(3) with n=180, k=5 and d=114.
This code was found by Heurico 1.16 in 0.00214 seconds.