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.