The generator matrix

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

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+204x^36+216x^39+216x^42+72x^45+20x^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 0.045 seconds.