The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+186x^36+252x^39+162x^42+108x^45+18x^48+2x^54

The gray image is a linear code over GF(3) with n=60, k=6 and d=36.
This code was found by Heurico 1.16 in 0.00354 seconds.