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.