The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X
0 X 0 0 0 0 X 2X 0 X 2X 2X X 2X 0 X
0 0 X 0 0 X 2X 0 X 2X X 2X 0 X X 0
0 0 0 X 0 2X 2X X 2X 2X 2X 2X X 2X X 2X
0 0 0 0 X 2X 2X 2X 0 0 2X X 0 X X X
generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+116x^27+162x^30+324x^33+114x^36+12x^45
The gray image is a linear code over GF(3) with n=48, k=6 and d=27.
This code was found by Heurico 1.16 in 0.0777 seconds.