The generator matrix

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

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+42x^18+18x^19+30x^20+120x^21+234x^22+228x^23+570x^24+774x^25+732x^26+1310x^27+2520x^28+1320x^29+2148x^30+3492x^31+1392x^32+1842x^33+1494x^34+672x^35+456x^36+216x^37+54x^39+18x^42

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 0.423 seconds.