The generator matrix
1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 0 1 2X+1 X 2 2 1 0 0
0 0 2X 0 0 0 0 0 0 0 0 2X X 2X 2X X 2X X 2X 0
0 0 0 X 0 0 0 0 X 2X X X 0 2X 0 2X 2X 0 2X X
0 0 0 0 X 0 0 X 2X 2X X 2X X 0 2X 0 0 X 0 X
0 0 0 0 0 2X 0 2X X 0 X 2X 0 0 X 2X 2X X 0 0
0 0 0 0 0 0 X 2X 0 2X 2X 2X 2X 2X 2X X 0 0 0 X
generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+66x^27+30x^29+192x^30+288x^32+400x^33+1404x^35+998x^36+3702x^38+1810x^39+4842x^41+1836x^42+2592x^44+938x^45+264x^47+202x^48+84x^51+22x^54+10x^57+2x^60
The gray image is a linear code over GF(3) with n=60, k=9 and d=27.
This code was found by Heurico 1.16 in 1.03 seconds.