The generator matrix

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

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+186x^112+306x^113+104x^114+396x^115+510x^116+146x^117+552x^118+552x^119+182x^120+468x^121+444x^122+62x^123+480x^124+378x^125+60x^126+408x^127+330x^128+76x^129+186x^130+204x^131+66x^132+186x^133+138x^134+16x^135+48x^136+36x^137+8x^138+6x^139+18x^140+2x^144+2x^147+2x^150+2x^156

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 64.1 seconds.