The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+72x^25+390x^26+378x^27+222x^28+408x^29+570x^30+468x^31+14202x^32+736x^33+540x^34+888x^35+404x^36+156x^37+150x^38+94x^39+2x^42+2x^48

The gray image is a linear code over GF(3) with n=144, k=9 and d=75.
This code was found by Heurico 1.16 in 85.7 seconds.