The generator matrix
1 0 1 1 1 1 1 0 1 1
0 1 1 2 0 1 2 1 0 0
0 0 2X 0 0 0 0 X X X
0 0 0 X 0 0 X 2X 2X 0
0 0 0 0 X 0 2X 2X X 2X
0 0 0 0 0 2X X 2X X X
generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+78x^12+288x^15+486x^16+492x^18+1944x^19+816x^21+1944x^22+468x^24+20x^27+24x^30
The gray image is a linear code over GF(3) with n=30, k=8 and d=12.
This code was found by Heurico 1.16 in 0.024 seconds.