The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  1  1  1  1  1
 0  1  1  2  0 2X+1  2  1  0 2X+1  X 2X+1  2 X+2 2X X+2
 0  0 2X  0  X 2X  X  0 2X  X 2X  0  0  X 2X  0
 0  0  0  X  X 2X 2X  X  0  0  X 2X  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+44x^27+102x^28+60x^30+144x^31+88x^33+216x^34+38x^36+24x^37+8x^42+4x^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 0.00301 seconds.