The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 0 1 X 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X X X 0 X 2X 0 2X 0 0
0 0 0 X 0 0 0 0 X 2X 2X X 2X X 2X X 2X X X 0 0
0 0 0 0 X 0 0 X 2X 2X 2X 0 X X X 2X 0 0 2X 2X 0
0 0 0 0 0 2X 0 2X X 2X 0 2X X 2X 0 2X 0 2X 0 2X 0
0 0 0 0 0 0 X 2X 0 X 2X X X 0 2X 0 0 2X 0 X 0
generates a code of length 21 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+36x^27+24x^29+116x^30+156x^32+184x^33+108x^34+540x^35+242x^36+864x^37+1410x^38+290x^39+2592x^40+2496x^41+344x^42+3456x^43+2538x^44+410x^45+1728x^46+1320x^47+278x^48+264x^50+164x^51+94x^54+18x^57+10x^60
The gray image is a linear code over GF(3) with n=63, k=9 and d=27.
This code was found by Heurico 1.16 in 1 seconds.