The generator matrix

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

generates a code of length 16 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+30x^29+40x^30+594x^32+24x^33+18x^35+14x^36+6x^38+2x^48

The gray image is a code over GF(3) with n=144, k=6 and d=87.
This code was found by Heurico 1.16 in 0.00165 seconds.