The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 X 1 0 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 2 1 0 0 2 1 2X+1 0 0
0 0 2X 0 0 0 0 0 0 2X X 0 0 2X X X 2X 2X X 0 2X X 0 0
0 0 0 X 0 0 0 0 0 2X 2X X X 0 2X 0 2X X 0 2X X X X 0
0 0 0 0 X 0 0 0 X 2X 2X 2X X 0 X 2X 0 X X 0 X X 2X 0
0 0 0 0 0 2X 0 0 2X 2X 0 2X X 2X 0 X 2X X X 2X X 0 X 0
0 0 0 0 0 0 X 0 X 2X 0 0 X 0 2X X 2X 2X 0 X 2X 0 X 0
0 0 0 0 0 0 0 X X X X X 0 X X 0 0 2X X 2X X X 0 0
generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+62x^30+18x^32+174x^33+108x^35+358x^36+108x^37+324x^38+898x^39+486x^40+936x^41+2842x^42+1620x^43+2268x^44+6702x^45+3510x^46+3348x^47+9678x^48+3888x^49+3096x^50+8022x^51+2754x^52+2160x^53+3110x^54+756x^55+864x^56+508x^57+294x^60+116x^63+32x^66+8x^69
The gray image is a linear code over GF(3) with n=72, k=10 and d=30.
This code was found by Heurico 1.16 in 9.68 seconds.