The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 X X 0 X 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 X 2X+1 2 1 2X+1 1 1 1 1 2X+1 X+2 2X+1 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X X X 2X 2X 2X 2X 2X 0 2X X X 0
0 0 0 X 0 0 0 0 X 2X X 2X X 2X 2X 0 0 X 2X 0 X 2X 0 0 X 2X 0 X X 0
0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X 2X 2X 2X X 0 0 0 0 0 0 X X X 0
0 0 0 0 0 2X 0 2X X 0 X X 2X 2X X 2X 0 0 0 X 2X 0 X 0 X X X 0 2X X
0 0 0 0 0 0 X 2X 0 2X 2X X X 2X 2X X 2X X X X 2X 2X X 2X X 0 0 2X 0 2X
generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.
Homogenous weight enumerator: w(x)=1x^0+40x^45+186x^48+30x^49+120x^50+506x^51+180x^52+216x^53+1064x^54+540x^55+846x^56+2074x^57+1110x^58+1128x^59+2826x^60+1386x^61+1188x^62+2558x^63+864x^64+720x^65+1204x^66+264x^67+156x^68+270x^69+142x^72+46x^75+16x^78+2x^81
The gray image is a linear code over GF(3) with n=90, k=9 and d=45.
This code was found by Heurico 1.16 in 2.18 seconds.