The generator matrix

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

generates a code of length 21 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+154x^27+274x^30+412x^33+748x^36+936x^39+4374x^40+1242x^42+8748x^43+1224x^45+816x^48+438x^51+220x^54+80x^57+14x^60+2x^63

The gray image is a linear code over GF(3) with n=63, k=9 and d=27.
This code was found by Heurico 1.16 in 1.67 seconds.