The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+56x^18+18x^20+186x^21+54x^22+180x^23+558x^24+432x^25+720x^26+2228x^27+1296x^28+1440x^29+4398x^30+1728x^31+1440x^32+3114x^33+864x^34+576x^35+222x^36+114x^39+54x^42+4x^45

The gray image is a linear code over GF(3) with n=45, k=9 and d=18.
This code was found by Heurico 1.16 in 0.422 seconds.