The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+88x^21+274x^24+622x^27+1042x^30+1916x^33+2748x^36+13122x^38+3504x^39+26244x^41+3456x^42+2838x^45+1772x^48+986x^51+352x^54+74x^57+10x^60

The gray image is a linear code over GF(3) with n=60, k=10 and d=21.
This code was found by Heurico 1.16 in 6.7 seconds.