The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 2X+1 0 2 1 X+2 2 0 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 X 2X X X X 2X 2X 2X 2X 0
0 0 0 X 0 0 0 0 X 2X X 2X 2X X 2X 2X 0 2X 0 0 2X 0
0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X 0 0 0 X 0 0
0 0 0 0 0 2X 0 2X X 0 X X X X 2X X X X 0 X 2X 0
0 0 0 0 0 0 X 2X 0 2X 2X X 2X X 2X 0 2X 2X X 2X 0 0
generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+74x^30+230x^33+90x^35+484x^36+216x^37+360x^38+1288x^39+756x^40+900x^41+2578x^42+1296x^43+1530x^44+3220x^45+1566x^46+1098x^47+2206x^48+540x^49+396x^50+616x^51+156x^54+50x^57+32x^60
The gray image is a linear code over GF(3) with n=66, k=9 and d=30.
This code was found by Heurico 1.16 in 1.24 seconds.