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  0  X  0  X 2X 2X 2X  0  0  X  X  X  X  0 2X 2X 2X  0
 0  0  X 2X 2X  X  0  X 2X  0  X 2X  X 2X  0  X  X 2X  0 2X

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 38.

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

The gray image is a linear code over GF(3) with n=60, k=4 and d=38.
This code was found by Heurico 1.16 in 0.00117 seconds.