The generator matrix

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

generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+164x^108+108x^109+306x^110+1146x^111+576x^112+738x^113+2344x^114+1008x^115+1212x^116+3384x^117+1410x^118+1626x^119+4606x^120+2100x^121+2046x^122+5146x^123+2430x^124+2256x^125+5620x^126+2208x^127+2232x^128+4948x^129+1818x^130+1644x^131+3410x^132+978x^133+792x^134+1426x^135+432x^136+210x^137+432x^138+42x^139+54x^140+126x^141+12x^142+6x^143+28x^144+8x^147+6x^150+6x^153+2x^156+2x^159

The gray image is a linear code over GF(3) with n=186, k=10 and d=108.
This code was found by Heurico 1.16 in 47 seconds.