The generator matrix

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

generates a code of length 15 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+126x^26+82x^27+216x^28+270x^29+730x^30+432x^31+162x^32+66x^33+90x^35+10x^36+2x^39

The gray image is a code over GF(3) with n=135, k=7 and d=78.
This code was found by Heurico 1.16 in 0.00532 seconds.