The generator matrix

 1  0  1  1  1  1  1 X+3  1  1  1  1  1 2X  1  X
 0  1 2X+4  8 X+3 X+1 X+2  1 2X 2X+8  4 X+1  4  1 2X+4  0
 0  0  3  0  3  6  6  6  0  0  6  6  3  0  3  6
 0  0  0  6  3  3  6  0  6  3  0  6  0  3  3  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+110x^27+324x^28+1184x^30+1296x^31+2178x^33+1296x^34+150x^36+20x^39+2x^48

The gray image is a code over GF(3) with n=144, k=8 and d=81.
This code was found by Heurico 1.16 in 0.0241 seconds.