The generator matrix

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

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+92x^21+18x^22+292x^24+144x^25+162x^26+758x^27+432x^28+648x^29+1226x^30+576x^31+648x^32+988x^33+288x^34+240x^36+32x^39+16x^42

The gray image is a linear code over GF(3) with n=45, k=8 and d=21.
This code was found by Heurico 1.16 in 0.427 seconds.