The generator matrix

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

generates a code of length 61 over Z3[X]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+360x^107+404x^108+1662x^110+1182x^111+3204x^113+1812x^114+4782x^116+2438x^117+5874x^119+3298x^120+6786x^122+3366x^123+6630x^125+3048x^126+5400x^128+2326x^129+2982x^131+1236x^132+1350x^134+452x^135+294x^137+106x^138+42x^140+12x^141+2x^153

The gray image is a linear code over GF(3) with n=183, k=10 and d=107.
This code was found by Heurico 1.16 in 51.2 seconds.