The generator matrix

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

generates a code of length 18 over Z3[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+270x^29+236x^30+858x^32+486x^33+1104x^35+670x^36+1476x^38+626x^39+618x^41+162x^42+48x^44+4x^45+2x^48

The gray image is a linear code over GF(3) with n=54, k=8 and d=29.
This code was found by Heurico 1.16 in 0.218 seconds.