The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 1 1 1 0 1 1 0 1 1 2X X X 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 X+1 1 0 2 X 2 2X+1 0 1 X X+2 1 X+1 2X+1 1 1 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 0 X 2X 0 2X 2X X X X 0 X 0 2X
0 0 0 X 0 0 0 0 0 0 0 2X 2X X X 0 X X 0 2X 2X 2X X 0 2X 0 X X 2X 0 2X X X 2X
0 0 0 0 X 0 0 0 X 2X 2X X X 0 0 2X 0 X X 2X X 2X X 0 X 0 X 2X 0 X 0 X 0 2X
0 0 0 0 0 2X 0 X 2X 2X 2X 0 2X 0 2X X X 2X X 2X 2X 0 2X X X X X 0 0 2X X X X 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X X 0 2X 2X 0 2X 2X 2X 0 X 0 0 2X X 0 2X X X X 2X X 2X
generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+138x^54+36x^56+392x^57+126x^58+168x^59+672x^60+216x^61+432x^62+1438x^63+810x^64+864x^65+2304x^66+1152x^67+1212x^68+2466x^69+1242x^70+1080x^71+2004x^72+648x^73+450x^74+1020x^75+180x^76+132x^77+306x^78+116x^81+64x^84+12x^87+2x^90
The gray image is a linear code over GF(3) with n=102, k=9 and d=54.
This code was found by Heurico 1.16 in 6.99 seconds.