The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 X 0 X X 0 X 2X 0 2X 2X X
0 0 X 0 2X X 2X 0 2X 2X 2X 2X 0 X 0
0 0 0 X 2X 2X 0 2X X X 0 0 2X 2X 2X
generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+52x^27+162x^30+26x^36+2x^45
The gray image is a linear code over GF(3) with n=45, k=5 and d=27.
This code was found by Heurico 1.16 in 0.00596 seconds.