The generator matrix

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

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+112x^27+432x^28+210x^30+324x^31+234x^33+486x^34+146x^36+216x^37+24x^39+2x^45

The gray image is a linear code over GF(3) with n=48, k=7 and d=27.
This code was found by Heurico 1.16 in 0.0448 seconds.