The generator matrix

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

generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+504x^56+540x^57+2046x^59+1398x^60+4530x^62+2570x^63+7476x^65+4026x^66+9030x^68+4980x^69+8922x^71+3806x^72+5028x^74+1960x^75+1614x^77+372x^78+210x^80+22x^81+6x^83+4x^84+4x^93

The gray image is a linear code over GF(3) with n=102, k=10 and d=56.
This code was found by Heurico 1.16 in 43.6 seconds.