The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+54x^21+60x^22+486x^23+574x^24+384x^25+1548x^26+1406x^27+1230x^28+2466x^29+2212x^30+1992x^31+3078x^32+1934x^33+696x^34+1152x^35+364x^36+12x^37+18x^38+2x^39+12x^42+2x^45

The gray image is a linear code over GF(3) with n=45, k=9 and d=21.
This code was found by Heurico 1.16 in 0.906 seconds.