The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 X 1 X 0 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 1 0 0 2X+1 1 1 2X+1 2 0 X 1 1 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 0 X 0 0 X 2X X 2X X X 0 X 2X 0 2X 0 0
0 0 0 X 0 0 0 0 0 2X 2X X X 2X X 0 X 2X 0 2X 2X 0 2X 0 2X X 2X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X X 2X 2X X 0 2X X 2X X X 0
0 0 0 0 0 2X 0 0 X X 2X 2X 0 2X X 2X 2X 2X 0 0 2X X X X 0 X 0 X 0
0 0 0 0 0 0 X 0 X 0 X X 2X 2X 2X X 2X X 2X 2X 0 2X 0 X 0 X 0 X 0
0 0 0 0 0 0 0 X X X 0 X X X 2X 0 2X 0 X 2X 0 X X 0 X 0 0 0 0
generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.
Homogenous weight enumerator: w(x)=1x^0+40x^39+6x^41+218x^42+6x^43+84x^44+308x^45+120x^46+432x^47+430x^48+702x^49+1392x^50+618x^51+2382x^52+3414x^53+758x^54+5502x^55+6066x^56+958x^57+8010x^58+7152x^59+1002x^60+6522x^61+5250x^62+798x^63+2640x^64+2088x^65+740x^66+360x^67+360x^68+400x^69+154x^72+98x^75+30x^78+6x^81+2x^84
The gray image is a linear code over GF(3) with n=87, k=10 and d=39.
This code was found by Heurico 1.16 in 14.7 seconds.