The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+22x^24+30x^25+48x^26+88x^27+54x^28+36x^29+176x^30+36x^31+54x^32+102x^33+24x^34+24x^35+10x^36+18x^37+4x^39+2x^42

The gray image is a linear code over GF(3) with n=45, k=6 and d=24.
This code was found by Heurico 1.16 in 0.00181 seconds.