The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 2 0 2X+1 0 0
0 0 2X 0 0 0 0 0 0 2X X 0 0 2X X X 0 X X 0
0 0 0 X 0 0 0 0 0 2X 2X X X 0 2X 0 2X 2X X 0
0 0 0 0 X 0 0 0 X 2X 2X 2X X 0 X 2X 0 X 2X 0
0 0 0 0 0 2X 0 0 2X 2X 0 2X X 2X 0 X 0 2X X 0
0 0 0 0 0 0 X 0 X 2X 0 0 X 0 2X X 2X X 0 0
0 0 0 0 0 0 0 X X X X X 0 X X 0 2X 0 0 0
generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+110x^24+18x^26+230x^27+180x^29+492x^30+756x^32+1690x^33+486x^34+1800x^35+5202x^36+2916x^37+2880x^38+9756x^39+5832x^40+3456x^41+9864x^42+3888x^43+2880x^44+4416x^45+1152x^47+576x^48+322x^51+114x^54+30x^57+2x^60
The gray image is a linear code over GF(3) with n=60, k=10 and d=24.
This code was found by Heurico 1.16 in 6.11 seconds.