The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 1 2 0 1 0 2 2 0 0
0 0 2X 0 0 0 0 0 0 2X X X 0 2X 0 X X 0 0 2X 2X 2X 0
0 0 0 X 0 0 0 0 0 0 2X X 2X 2X X 2X 0 2X 0 0 2X X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X X X X
0 0 0 0 0 2X 0 0 X 2X 0 2X X 2X X 2X 0 X 0 X 0 0 X
0 0 0 0 0 0 X 0 X 0 X 0 2X 2X 0 X 2X X 0 X 2X X X
0 0 0 0 0 0 0 X X X X 2X 0 0 X X 2X X 2X 0 0 X 2X
generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+108x^30+310x^33+18x^34+658x^36+216x^37+162x^38+1990x^39+1080x^40+1296x^41+5270x^42+2880x^43+3888x^44+9176x^45+4320x^46+5184x^47+9020x^48+3456x^49+2592x^50+4604x^51+1152x^52+1168x^54+326x^57+130x^60+40x^63+4x^66
The gray image is a linear code over GF(3) with n=69, k=10 and d=30.
This code was found by Heurico 1.16 in 9.61 seconds.