The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 X 0 1 1 1 0 X 0
0 1 1 2 0 1 2 1 0 2 2X+1 1 1 1 0 2X+1 2 1 1 1
0 0 2X 0 0 0 0 X X 0 0 2X X 2X 2X X 0 2X 0 X
0 0 0 X 0 0 0 2X X 2X 2X 2X 0 0 X X 2X X X 0
0 0 0 0 X 0 X 2X 0 X 0 2X 0 X 2X 0 2X X 2X 0
0 0 0 0 0 2X 2X 2X 0 0 2X 0 X 2X X 2X 0 0 X 2X
generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+98x^30+54x^32+198x^33+432x^35+328x^36+1296x^38+552x^39+1728x^41+504x^42+864x^44+322x^45+138x^48+36x^51+6x^54+4x^57
The gray image is a linear code over GF(3) with n=60, k=8 and d=30.
This code was found by Heurico 1.16 in 0.163 seconds.