The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+222x^19+318x^20+956x^21+1524x^22+1782x^23+4354x^24+5862x^25+7344x^26+15812x^27+14382x^28+19020x^29+27548x^30+18294x^31+19170x^32+19672x^33+10338x^34+4374x^35+3762x^36+1866x^37+480x^38+62x^39+4x^42

The gray image is a linear code over GF(3) with n=45, k=11 and d=19.
This code was found by Heurico 1.16 in 66.8 seconds.