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 1 1 0 1 1 2X^2+X 1 1 1 1 1 1 1 1 2X^2+X 1 1 1 1 0 1 1 1 1 2X X^2+X 1 0 1 X^2 1 1 1 1 1 1 1 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 0 2X^2+X+2 1 2X^2+2X+1 2X+2 1 X^2+2 2X^2+X 2X^2+2X+1 2X X+1 2X^2+1 2X 2X+2 1 2X^2+X+2 2X^2+X+2 2 2X 1 2X^2+X X^2+X+2 X^2+2X 0 1 1 2 1 2X^2+X 1 0 X^2+X 2X^2+2X+1 X+1 X^2+2X+1 2X^2+1 X^2+1 2 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 2X^2 0 X^2 0 0 X^2 2X^2 2X^2 X^2 0 2X^2 0 X^2 0 0 0 2X^2 0 X^2 X^2 X^2 2X^2 2X^2 0 2X^2 X^2 0 0 2X^2 0 2X^2 X^2 0 X^2 0 X^2 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 2X^2 0 X^2 0 2X^2 0 2X^2 0 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 0 0 0 X^2 2X^2 X^2 X^2 2X^2 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 X^2 2X^2 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 0 X^2 X^2 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 X^2 2X^2 0 X^2 0 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 2X^2 0 0 0 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 0 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 2X^2 0 0 X^2 2X^2 2X^2 0 0 0 X^2 X^2 X^2 0 2X^2 X^2 2X^2 0 2X^2 X^2 0 2X^2 0 2X^2 0 X^2 generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 117. Homogenous weight enumerator: w(x)=1x^0+82x^117+18x^118+96x^119+300x^120+690x^121+492x^122+954x^123+2148x^124+2052x^125+1808x^126+6210x^127+5232x^128+3618x^129+8772x^130+6792x^131+3322x^132+7224x^133+3816x^134+1690x^135+2520x^136+390x^137+374x^138+96x^139+60x^140+122x^141+24x^142+18x^143+50x^144+6x^146+20x^147+22x^150+10x^153+8x^156+6x^159+4x^162+2x^168 The gray image is a linear code over GF(3) with n=585, k=10 and d=351. This code was found by Heurico 1.16 in 9.91 seconds.