The generator matrix

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

generates a code of length 16 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+108x^28+364x^30+444x^31+162x^32+670x^33+408x^34+14x^36+12x^37+2x^39+2x^42

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 0.0036 seconds.