The generator matrix

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

generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+174x^106+306x^107+834x^108+822x^109+1230x^110+2218x^111+2124x^112+2412x^113+4346x^114+3996x^115+4416x^116+7054x^117+5946x^118+6684x^119+10092x^120+7746x^121+8700x^122+12404x^123+9402x^124+9882x^125+13324x^126+8904x^127+8514x^128+10758x^129+6870x^130+5844x^131+6712x^132+4122x^133+3120x^134+3094x^135+1788x^136+1062x^137+1078x^138+486x^139+270x^140+206x^141+72x^142+42x^143+32x^144+36x^145+6x^146+8x^147+2x^150+4x^153+2x^156+2x^171

The gray image is a linear code over GF(3) with n=186, k=11 and d=106.
This code was found by Heurico 1.16 in 494 seconds.