The generator matrix

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

generates a code of length 16 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+32x^24+156x^26+92x^27+810x^28+618x^29+1662x^30+3240x^31+5634x^32+3128x^33+3240x^34+834x^35+132x^36+48x^38+48x^39+8x^42

The gray image is a code over GF(3) with n=144, k=9 and d=72.
This code was found by Heurico 1.16 in 0.174 seconds.