The generator matrix

 1  0  0  1  1  1  1  1  1 2X+6  1  1  1  1 2X  1
 0  1  0 2X+6  1 2X+7  8  3 X+8  1 X+6 2X+4 X+4 2X+8  1 2X
 0  0  1 2X+7  1 2X+6 2X+8  5  X  7 2X 2X+2  3 X+1 X+4  0

generates a code of length 16 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+136x^27+738x^28+1320x^29+2116x^30+2328x^31+4974x^32+3888x^33+2580x^34+1320x^35+250x^36+24x^37+8x^39

The gray image is a code over GF(3) with n=144, k=9 and d=81.
This code was found by Heurico 1.16 in 0.16 seconds.