The generator matrix

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

generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+56x^105+54x^106+48x^107+304x^108+390x^109+264x^110+768x^111+978x^112+684x^113+1174x^114+1830x^115+1044x^116+1996x^117+2856x^118+1656x^119+2740x^120+4224x^121+2124x^122+3160x^123+4878x^124+2502x^125+3240x^126+4548x^127+2358x^128+2852x^129+3684x^130+1512x^131+1878x^132+1836x^133+618x^134+894x^135+684x^136+258x^137+344x^138+240x^139+54x^140+148x^141+42x^142+58x^144+40x^147+10x^150+14x^153+6x^156

The gray image is a linear code over GF(3) with n=186, k=10 and d=105.
This code was found by Heurico 1.16 in 45.3 seconds.