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.