The generator matrix

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

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+58x^24+78x^25+306x^26+226x^27+300x^28+522x^29+620x^30+396x^31+1134x^32+810x^33+444x^34+774x^35+430x^36+222x^37+180x^38+28x^39+18x^40+14x^42

The gray image is a linear code over GF(3) with n=48, k=8 and d=24.
This code was found by Heurico 1.16 in 0.115 seconds.