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.