The generator matrix

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

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+44x^111+48x^112+150x^113+100x^114+258x^115+282x^116+120x^117+372x^118+396x^119+102x^120+438x^121+492x^122+70x^123+594x^124+564x^125+66x^126+546x^127+498x^128+58x^129+432x^130+378x^131+48x^132+174x^133+126x^134+20x^135+54x^136+24x^137+30x^138+6x^140+22x^141+12x^144+14x^147+10x^150+6x^153+4x^156+2x^159

The gray image is a linear code over GF(3) with n=186, k=8 and d=111.
This code was found by Heurico 1.16 in 0.703 seconds.