The generator matrix

 1  0  0  1  1  1  1  1  1  0  1  1  0 2X  1  1  1  1  1 2X  1  1  0  1 2X  1  1 2X  1
 0  1  0  0  0 2X+1  2  1  2  1 2X+1 2X+2  1  1 X+2 2X+1  2 2X X+2  0  X 2X+2  X 2X  1 X+1 X+2  1 X+2
 0  0  1  1  2 2X+2  2  1  0 X+2 2X 2X+1  0 2X+1 2X 2X+1 2X+2  1 2X+1  1 X+2  0  1  1 X+1 2X X+2  X 2X+1
 0  0  0 2X  0 2X  0  X  X  X 2X 2X  X  0  0  X  0 2X  X  X 2X  0 2X 2X  X 2X  X  0  0
 0  0  0  0  X 2X 2X 2X  0  X  X  0 2X  X 2X  0  0 2X 2X 2X  0  X  0  X  0 2X 2X 2X  X

generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+144x^49+300x^51+540x^52+390x^54+972x^55+432x^57+1026x^58+588x^60+1026x^61+330x^63+540x^64+108x^66+126x^67+30x^69+6x^72+2x^81

The gray image is a linear code over GF(3) with n=87, k=8 and d=49.
This code was found by Heurico 1.16 in 0.668 seconds.