The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X 2X  0 X+3 2X X+3  0  6 2X+6  0  6 X+3  6 X+3 2X
 0  0  6  0  6  0  3  6  3  3  6  3  3  6  3  0
 0  0  0  6  3  6  6  3  3  3  0  6  3  0  0  0

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+86x^27+384x^30+972x^32+612x^33+114x^36+12x^39+6x^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 0.00644 seconds.