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

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+378x^56+490x^57+558x^58+1434x^59+1402x^60+1206x^61+3018x^62+2640x^63+2142x^64+4692x^65+4130x^66+2880x^67+6096x^68+4850x^69+3084x^70+6012x^71+3854x^72+2406x^73+3498x^74+1838x^75+702x^76+930x^77+422x^78+120x^79+186x^80+46x^81+24x^82+4x^84+4x^87+2x^90

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 504 seconds.