The generator matrix

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

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+80x^24+96x^25+114x^26+304x^27+120x^28+144x^29+428x^30+144x^31+180x^32+334x^33+102x^34+48x^35+64x^36+24x^37+4x^39

The gray image is a linear code over GF(3) with n=45, k=7 and d=24.
This code was found by Heurico 1.13 in 0.0054 seconds.