The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+234x^29+516x^30+180x^32+1014x^33+234x^35+6x^36+2x^45

The gray image is a linear code over GF(3) with n=144, k=7 and d=87.
This code was found by Heurico 1.16 in 52.7 seconds.