The generator matrix

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

generates a code of length 64 over Z3[X]/(X^2) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+534x^113+390x^114+1722x^116+1234x^117+3108x^119+2150x^120+4608x^122+2274x^123+5976x^125+3012x^126+6876x^128+3214x^129+6480x^131+3066x^132+5076x^134+2482x^135+3060x^137+1256x^138+1482x^140+480x^141+348x^143+100x^144+78x^146+20x^147+18x^149+2x^153+2x^165

The gray image is a linear code over GF(3) with n=192, k=10 and d=113.
This code was found by Heurico 1.16 in 118 seconds.