The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X
0 3 0 3 0 3 6 6 6 0 0 3 3 0 3
0 0 3 6 6 3 0 3 6 0 3 6 0 3 6
generates a code of length 15 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+22x^27+192x^30+24x^33+4x^36
The gray image is a code over GF(3) with n=135, k=5 and d=81.
This code was found by Heurico 1.16 in 0.000642 seconds.