The generator matrix
1 0 1 1 1 1 1 0 1 1 1 1
0 1 1 2 0 1 2 1 0 0 0 0
0 0 2X 0 0 0 0 0 X X X 0
0 0 0 X 0 0 0 X 2X 2X 2X X
0 0 0 0 X 0 0 2X 2X X 2X 2X
0 0 0 0 0 2X 0 2X 2X 2X X X
0 0 0 0 0 0 X X X 0 X 0
generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+50x^12+188x^15+560x^18+1458x^20+1412x^21+5832x^23+1964x^24+5832x^26+1612x^27+644x^30+116x^33+14x^36
The gray image is a linear code over GF(3) with n=36, k=9 and d=12.
This code was found by Heurico 1.16 in 0.168 seconds.