The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  X  X  X  0  X  0
 0  0  X  0  0  0  0  0  0 2X  X 2X 2X  0  0
 0  0  0  X  0  0  0  0  X 2X  0 2X  X 2X  0
 0  0  0  0  X  0  0  0 2X 2X  0  X  0 2X  0
 0  0  0  0  0  X  0  0 2X 2X  X  0 2X  X  0
 0  0  0  0  0  0  X  0 2X 2X 2X  X  X  X  0
 0  0  0  0  0  0  0  X 2X  0  X 2X  X  0  X

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+94x^15+198x^18+372x^21+774x^24+1082x^27+14430x^30+1248x^33+882x^36+426x^39+152x^42+24x^45

The gray image is a linear code over GF(3) with n=45, k=9 and d=15.
This code was found by Heurico 1.16 in 0.347 seconds.