The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+54x^22+90x^23+294x^24+186x^25+180x^26+724x^27+372x^28+540x^29+1466x^30+468x^31+450x^32+1028x^33+336x^34+198x^35+112x^36+42x^37+10x^39+10x^42

The gray image is a linear code over GF(3) with n=45, k=8 and d=22.
This code was found by Heurico 1.16 in 3.54 seconds.