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

generates a code of length 18 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+108x^24+18x^26+238x^27+54x^28+180x^29+770x^30+432x^31+720x^32+2246x^33+1296x^34+1440x^35+3830x^36+1728x^37+1440x^38+2852x^39+864x^40+576x^41+656x^42+170x^45+50x^48+14x^51

The gray image is a linear code over GF(3) with n=54, k=9 and d=24.
This code was found by Heurico 1.16 in 0.802 seconds.