The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X
0 X 0 X^2 2X 2X^2+X X 2X 2X X^2+2X 2X^2+X 2X^2 X 2X^2+2X 2X^2 0
0 0 X 2X^2+2X X^2 X^2+2X X X^2+X 2X^2+2X X^2 X^2 X^2+2X X^2+2X 2X^2+X X 2X
generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+108x^28+108x^29+190x^30+72x^31+1098x^32+372x^33+72x^34+72x^35+72x^37+18x^38+2x^39+2x^45
The gray image is a linear code over GF(3) with n=144, k=7 and d=84.
This code was found by Heurico 1.16 in 0.34 seconds.