The generator matrix

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

generates a code of length 18 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+86x^21+248x^24+408x^27+678x^30+1104x^33+4374x^34+1350x^36+8748x^37+1176x^39+864x^42+426x^45+166x^48+52x^51+2x^54

The gray image is a linear code over GF(3) with n=54, k=9 and d=21.
This code was found by Heurico 1.16 in 0.943 seconds.