The generator matrix

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

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+20x^27+78x^30+124x^33+8x^36+8x^42+4x^45

The gray image is a linear code over GF(3) with n=48, k=5 and d=27.
This code was found by Heurico 1.16 in 0.00101 seconds.