The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+132x^20+128x^21+672x^22+1086x^23+946x^24+2154x^25+3360x^26+3130x^27+6048x^28+7134x^29+6398x^30+8382x^31+7320x^32+4018x^33+4146x^34+2616x^35+674x^36+468x^37+222x^38+8x^39+4x^42+2x^45

The gray image is a linear code over GF(3) with n=45, k=10 and d=20.
This code was found by Heurico 1.16 in 7.06 seconds.