The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  1
 0  1  1  2  0  1  2  1  0 2X+1  2  1  0 2X+1  2  0 2X+1  0
 0  0 2X  0  0  0  0  0  0 2X  X  0  0  X  X 2X 2X  0
 0  0  0  X  0  0  0  0  0 2X 2X  X  X 2X  X  X 2X  0
 0  0  0  0  X  0  0  0  X 2X 2X 2X  X  0 2X 2X 2X  0
 0  0  0  0  0 2X  0  0 2X 2X  0 2X  X  X  X  X 2X  X
 0  0  0  0  0  0  X  0  X 2X  0  0  X 2X  X  0  X 2X
 0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  X 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+78x^21+306x^24+54x^26+664x^27+162x^28+540x^29+2002x^30+1296x^31+2160x^32+6982x^33+3888x^34+4320x^35+11854x^36+5184x^37+4320x^38+8164x^39+2592x^40+1728x^41+2110x^42+412x^45+178x^48+52x^51+2x^54

The gray image is a linear code over GF(3) with n=54, k=10 and d=21.
This code was found by Heurico 1.16 in 4.53 seconds.