The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+28x^27+78x^30+32x^33+1944x^34+38x^36+30x^39+20x^42+14x^45+2x^51

The gray image is a linear code over GF(3) with n=153, k=7 and d=81.
This code was found by Heurico 1.16 in 0.00861 seconds.