The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0  6  0  0  0  0  6  3  0  6  3  3  6  3  0  6
 0  0  6  0  0  6  3  0  6  3  6  3  0  6  6  0
 0  0  0  6  0  3  3  6  3  3  3  3  6  3  6  3
 0  0  0  0  6  3  3  3  0  0  3  6  0  6  6  6

generates a code of length 16 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+116x^27+162x^30+1458x^32+324x^33+114x^36+12x^45

The gray image is a code over GF(3) with n=144, k=7 and d=81.
This code was found by Heurico 1.16 in 0.161 seconds.