The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+58x^12+202x^15+572x^18+1140x^21+2346x^24+3296x^27+43284x^30+3666x^33+2622x^36+1364x^39+428x^42+70x^45

The gray image is a linear code over GF(3) with n=45, k=10 and d=12.
This code was found by Heurico 1.16 in 1.84 seconds.