The generator matrix

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

generates a code of length 61 over Z3[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+462x^110+446x^111+1302x^113+690x^114+1728x^116+984x^117+1932x^119+948x^120+2394x^122+1130x^123+2028x^125+942x^126+1614x^128+816x^129+1032x^131+410x^132+396x^134+164x^135+204x^137+22x^138+24x^140+2x^141+6x^143+6x^144

The gray image is a linear code over GF(3) with n=183, k=9 and d=110.
This code was found by Heurico 1.16 in 13.2 seconds.