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.