The generator matrix

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

generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+216x^46+336x^47+422x^48+990x^49+1326x^50+1392x^51+2430x^52+3030x^53+2328x^54+3960x^55+4722x^56+3864x^57+5670x^58+5874x^59+4092x^60+5400x^61+4662x^62+2368x^63+2412x^64+1638x^65+714x^66+738x^67+252x^68+114x^69+54x^70+30x^71+10x^72+4x^75

The gray image is a linear code over GF(3) with n=87, k=10 and d=46.
This code was found by Heurico 1.16 in 16.5 seconds.