The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 X 1 1 1 X 1
0 X 0 0 0 0 0 0 0 0 X X X 0 X X 0 X X 2X 2X X 2X X 0 X X X 2X
0 0 X 0 0 0 0 0 X X 2X 2X 2X 0 X X 2X 0 X 0 2X X 0 X X 0 2X X 0
0 0 0 X 0 0 0 X 2X 2X 2X X X 0 0 X 0 2X 0 0 0 2X X X 2X X 0 0 X
0 0 0 0 X 0 0 2X 2X X X 0 2X X 0 0 X 0 2X 2X X X 0 0 X X 2X X 0
0 0 0 0 0 X 0 2X X 2X X 2X 0 X X 2X 2X X 2X X 2X 2X 2X X 0 X 2X X 0
0 0 0 0 0 0 X X 0 X 0 X 0 X 2X 0 2X 2X X 0 0 2X 2X X X X 2X 2X 0
generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.
Homogenous weight enumerator: w(x)=1x^0+152x^45+192x^48+246x^51+162x^52+242x^54+972x^55+270x^57+1944x^58+324x^60+1296x^61+312x^63+216x^66+126x^69+76x^72+24x^75+6x^78
The gray image is a linear code over GF(3) with n=87, k=8 and d=45.
This code was found by Heurico 1.16 in 3.95 seconds.