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

generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+330x^109+576x^110+254x^111+1170x^112+1446x^113+458x^114+2088x^115+2520x^116+696x^117+2976x^118+3318x^119+898x^120+3936x^121+4188x^122+1060x^123+4518x^124+4662x^125+1148x^126+4584x^127+4092x^128+948x^129+3486x^130+3054x^131+676x^132+2052x^133+1656x^134+328x^135+798x^136+546x^137+58x^138+264x^139+168x^140+20x^141+36x^142+18x^143+14x^144+6x^145+2x^147

The gray image is a linear code over GF(3) with n=186, k=10 and d=109.
This code was found by Heurico 1.16 in 91.5 seconds.