The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+110x^111+30x^112+54x^113+174x^114+192x^115+192x^116+340x^117+228x^118+186x^119+1562x^120+186x^121+1674x^122+4662x^123+156x^124+3180x^125+4656x^126+282x^127+276x^128+446x^129+204x^130+216x^131+248x^132+84x^133+30x^134+80x^135+84x^136+24x^137+26x^138+12x^139+44x^141+18x^144+14x^147+2x^150+6x^153+2x^156+2x^171

The gray image is a linear code over GF(3) with n=558, k=9 and d=333.
This code was found by Heurico 1.16 in 2.2 seconds.