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

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+294x^109+450x^110+480x^111+984x^112+1344x^113+1034x^114+1794x^115+1998x^116+1682x^117+2448x^118+2874x^119+2168x^120+3198x^121+3426x^122+2718x^123+3696x^124+3612x^125+2644x^126+3786x^127+3672x^128+2076x^129+2976x^130+2460x^131+1478x^132+1860x^133+1374x^134+750x^135+636x^136+540x^137+222x^138+168x^139+96x^140+42x^141+30x^142+18x^143+8x^144+6x^146+4x^147+2x^150

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 69 seconds.