The generator matrix

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

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+162x^112+390x^113+436x^114+756x^115+900x^116+830x^117+1386x^118+1662x^119+1472x^120+2412x^121+2586x^122+1936x^123+2850x^124+3144x^125+2214x^126+3846x^127+3750x^128+2818x^129+3648x^130+3846x^131+2318x^132+3096x^133+2964x^134+1952x^135+2220x^136+1734x^137+874x^138+1068x^139+666x^140+336x^141+372x^142+174x^143+58x^144+54x^145+36x^146+26x^147+18x^149+12x^150+12x^153+12x^156+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 48.7 seconds.