The generator matrix
1 0 1 1 1 1 1 0 1 1 1 1 1 X 1
0 1 1 2 2X+1 0 2 1 X X 2X+1 X+1 0 X X+1
0 0 2X 0 X X 2X 2X X 0 2X X 2X 2X 0
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+76x^27+100x^30+48x^33+16x^36+2x^39
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 0.00076 seconds.