The generator matrix

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

generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+168x^55+282x^56+414x^57+798x^58+1098x^59+1104x^60+1980x^61+2448x^62+1992x^63+3390x^64+4122x^65+3274x^66+5088x^67+5262x^68+3666x^69+5172x^70+4866x^71+3104x^72+3504x^73+2886x^74+1346x^75+1566x^76+822x^77+336x^78+192x^79+84x^80+40x^81+12x^82+20x^84+6x^87+2x^90+4x^93

The gray image is a linear code over GF(3) with n=102, k=10 and d=55.
This code was found by Heurico 1.16 in 23.2 seconds.