The generator matrix

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

generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+6x^44+142x^45+6x^46+78x^47+390x^48+72x^49+288x^50+824x^51+360x^52+564x^53+1800x^54+960x^55+942x^56+2638x^57+1440x^58+1206x^59+2620x^60+1152x^61+834x^62+1690x^63+384x^64+384x^65+574x^66+72x^68+172x^69+66x^72+16x^75+2x^78

The gray image is a linear code over GF(3) with n=87, k=9 and d=44.
This code was found by Heurico 1.16 in 50.2 seconds.