The generator matrix

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

generates a code of length 16 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+108x^28+108x^29+190x^30+72x^31+1098x^32+372x^33+72x^34+72x^35+72x^37+18x^38+2x^39+2x^45

The gray image is a code over GF(3) with n=144, k=7 and d=84.
This code was found by Heurico 1.16 in 0.34 seconds.