The generator matrix

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

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+116x^45+114x^46+252x^47+742x^48+774x^49+1062x^50+2052x^51+1782x^52+2196x^53+3814x^54+3354x^55+4014x^56+5964x^57+4770x^58+4932x^59+5872x^60+4194x^61+3474x^62+4038x^63+2040x^64+1404x^65+1206x^66+450x^67+162x^68+208x^69+18x^70+28x^72+8x^75+4x^78+4x^81

The gray image is a linear code over GF(3) with n=87, k=10 and d=45.
This code was found by Heurico 1.16 in 15.9 seconds.