The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+156x^24+102x^25+300x^26+500x^27+2142x^28+1554x^29+5208x^30+9258x^31+17946x^32+9960x^33+8682x^34+1986x^35+804x^36+216x^37+84x^38+120x^39+12x^40+18x^42

The gray image is a linear code over GF(3) with n=144, k=10 and d=72.
This code was found by Heurico 1.16 in 1.45 seconds.