The generator matrix

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

generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+132x^111+300x^112+282x^113+546x^114+894x^115+474x^116+772x^117+1188x^118+636x^119+1008x^120+1398x^121+720x^122+982x^123+1350x^124+666x^125+1020x^126+1326x^127+672x^128+964x^129+1062x^130+528x^131+700x^132+828x^133+246x^134+320x^135+312x^136+132x^137+90x^138+66x^139+18x^140+22x^141+24x^142+2x^144+2x^156

The gray image is a linear code over GF(3) with n=186, k=9 and d=111.
This code was found by Heurico 1.16 in 6.8 seconds.