The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+156x^26+128x^27+54x^28+336x^29+852x^30+216x^31+2376x^32+1512x^33+216x^34+420x^35+132x^36+114x^38+48x^39

The gray image is a linear code over GF(3) with n=144, k=8 and d=78.
This code was found by Heurico 1.16 in 0.058 seconds.