The generator matrix

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

generates a code of length 61 over Z3[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+102x^112+264x^113+236x^114+408x^115+420x^116+366x^117+498x^118+438x^119+276x^120+396x^121+414x^122+240x^123+360x^124+294x^125+228x^126+264x^127+246x^128+188x^129+192x^130+204x^131+94x^132+114x^133+96x^134+56x^135+66x^136+36x^137+16x^138+30x^139+18x^140

The gray image is a linear code over GF(3) with n=183, k=8 and d=112.
This code was found by Heurico 1.16 in 0.594 seconds.