The generator matrix

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

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+52x^15+18x^16+180x^18+108x^19+354x^21+432x^22+1668x^24+1584x^25+1458x^26+7028x^27+3564x^28+5832x^29+13152x^30+4104x^31+5832x^32+9018x^33+2448x^34+798x^36+864x^37+426x^39+116x^42+12x^45

The gray image is a linear code over GF(3) with n=45, k=10 and d=15.
This code was found by Heurico 1.16 in 1.63 seconds.