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

generates a code of length 64 over Z3[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+66x^112+270x^113+526x^114+642x^115+792x^116+1414x^117+1206x^118+1440x^119+2238x^120+1776x^121+2088x^122+3138x^123+2328x^124+2538x^125+3918x^126+2814x^127+2814x^128+4102x^129+3318x^130+2982x^131+3680x^132+2544x^133+2310x^134+2742x^135+1728x^136+1356x^137+1384x^138+792x^139+672x^140+714x^141+228x^142+210x^143+174x^144+48x^145+24x^146+16x^147+6x^148+4x^150+4x^153+2x^159

The gray image is a linear code over GF(3) with n=192, k=10 and d=112.
This code was found by Heurico 1.16 in 49 seconds.