The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 X 1 X 1
0 X 0 0 0 0 0 0 0 0 X X X X X 2X 2X 2X 0 2X 2X X 0 X X 0 X 0 0 0
0 0 X 0 0 0 0 0 X X 2X 2X 2X X 2X 0 2X 2X X 0 2X 0 0 X X X 2X 0 X 0
0 0 0 X 0 0 0 X 2X 2X 2X X X 0 0 X 0 0 X 0 2X X X 0 2X X 0 X 2X 0
0 0 0 0 X 0 0 2X 2X X X 0 2X 2X 2X X 0 0 0 X 2X X 0 2X X 2X X 0 X 0
0 0 0 0 0 X 0 2X X 2X X 2X 0 2X 2X 0 0 X X 2X X X 2X X 0 0 2X X 2X 0
0 0 0 0 0 0 X X 0 X 0 X 0 2X 0 2X 2X 0 2X X 0 X X X X 2X X 2X 2X 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+52x^45+160x^48+222x^51+54x^52+228x^54+432x^55+262x^57+1296x^58+322x^60+1728x^61+262x^63+864x^64+274x^66+202x^69+132x^72+60x^75+10x^78
The gray image is a linear code over GF(3) with n=90, k=8 and d=45.
This code was found by Heurico 1.16 in 0.415 seconds.