The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  2  0 2X+1  2  1  0 2X+1  X 2X+1  X  0 2X+1 X+1 2X  1  X  1
 0  0 2X  0  X 2X  X  0 2X  X 2X  0 2X  0  X  X  0 2X  X  0
 0  0  0  X  X 2X 2X  X  0  0  X 2X 2X  X  X 2X 2X  X  0  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+180x^36+260x^39+168x^42+100x^45+16x^48+4x^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 0.11 seconds.