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.