The generator matrix 1 0 1 1 1 1 1 2X^2+X 1 2X 1 1 1 1 0 1 1 2X^2+X 1 1 2X 1 1 1 1 1 2X 2X^2+X 1 1 0 1 1 1 1 2X^2+X 2X 0 1 1 X^2+X 1 2X^2+X 1 2X^2+X 1 1 1 1 1 1 1 1 1 1 0 X^2 1 1 2X X^2+2X 1 0 1 2X^2+2X+1 2 2X^2+X X+1 2X^2+X+2 1 2X^2+1 1 2X 2X+2 2 0 1 2X^2+2X+1 2X^2+X+2 1 X+1 2X^2+X 1 2X^2+1 2X 2X+2 2 2X^2+1 1 1 2X+2 2X^2+2X+1 1 2X 2X^2+X 2X^2+1 2 1 1 1 0 2X^2+X 1 X+1 1 2X^2+1 1 2X+2 2X^2+2X+1 X+1 2X^2+2X+1 X^2+2X+1 0 X^2 2X+2 2 X^2+2X+2 1 1 0 2X^2+X+2 1 1 0 0 0 2X^2 0 0 0 2X^2 2X^2 X^2 2X^2 2X^2 0 X^2 0 X^2 X^2 X^2 0 2X^2 X^2 2X^2 0 X^2 X^2 2X^2 0 X^2 X^2 0 0 X^2 2X^2 X^2 0 0 2X^2 2X^2 0 X^2 2X^2 X^2 0 2X^2 0 2X^2 0 2X^2 X^2 X^2 0 X^2 0 0 X^2 0 2X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 2X^2 2X^2 0 X^2 0 X^2 0 X^2 2X^2 2X^2 0 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 0 2X^2 0 X^2 2X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 2X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 2X^2 X^2 X^2 0 2X^2 2X^2 0 0 0 0 0 0 0 2X^2 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 0 0 0 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 X^2 0 2X^2 0 0 2X^2 0 0 2X^2 X^2 0 0 0 0 0 X^2 X^2 2X^2 0 2X^2 X^2 2X^2 2X^2 0 0 2X^2 X^2 X^2 0 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 2X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 0 X^2 0 2X^2 0 0 2X^2 X^2 0 2X^2 0 X^2 0 2X^2 X^2 0 2X^2 2X^2 0 X^2 0 2X^2 0 2X^2 2X^2 X^2 2X^2 0 2X^2 X^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+64x^111+12x^112+168x^113+330x^114+456x^115+564x^116+804x^117+2070x^118+2238x^119+1882x^120+5856x^121+4932x^122+3568x^123+9846x^124+6630x^125+3532x^126+7644x^127+3570x^128+1736x^129+1692x^130+720x^131+288x^132+120x^133+96x^134+86x^135+6x^136+24x^137+26x^138+12x^140+18x^141+30x^144+14x^147+8x^150+2x^153+4x^156 The gray image is a linear code over GF(3) with n=558, k=10 and d=333. This code was found by Heurico 1.16 in 9.37 seconds.