The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 X 0 X 2X 2X 2X 0 0 X
0 0 X 2X 2X X 0 X 2X 0 X 2X
generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.
Homogenous weight enumerator: w(x)=1x^0+6x^21+66x^24+6x^27+2x^36
The gray image is a linear code over GF(3) with n=36, k=4 and d=21.
This code was found by Heurico 1.16 in 0.000324 seconds.