The generator matrix

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

generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+114x^64+162x^65+40x^66+90x^67+84x^68+20x^69+54x^70+24x^71+14x^72+42x^73+30x^74+2x^75+12x^76+18x^77+2x^78+12x^79+6x^80+2x^87

The gray image is a linear code over GF(3) with n=102, k=6 and d=64.
This code was found by Heurico 1.16 in 0.328 seconds.