The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1
0 X 0 0 0 0 X 2X 2X 0 X 0 X 2X X 0 X X
0 0 X 0 0 X 2X 0 2X 0 2X X 2X 2X 0 X 2X X
0 0 0 X 0 2X 2X X 0 X X 2X 0 2X 0 0 2X 2X
0 0 0 0 X 2X 2X 2X 2X 2X 2X 0 0 2X 2X X 0 0
generates a code of length 18 over Z3[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+52x^30+76x^33+162x^34+22x^36+324x^37+40x^39+28x^42+4x^45+16x^48+4x^51
The gray image is a linear code over GF(3) with n=54, k=6 and d=30.
This code was found by Heurico 1.16 in 0.0375 seconds.