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 1 0 1 X^2+X 1 2X^2+X 1 1 1 1 0 1 2X^2+X 1 1 1 1 1 1 1 1 2X X^2 1 X^2+2X X 1 2X^2+X 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 1 2X+2 2X^2+2X+1 1 2X 2X^2+X 2X^2+1 2 1 1 0 1 2X^2+X 1 X+1 1 0 2X^2+X+2 2 2X^2+X+2 1 0 1 2X^2+1 X^2+2 X^2+1 2X+2 X^2 2X^2+1 X^2+X X^2+1 1 1 0 1 1 2X 1 2 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 X^2 0 2X^2 X^2 0 2X^2 X^2 X^2 0 0 0 2X^2 2X^2 2X^2 X^2 X^2 0 X^2 0 0 2X^2 X^2 2X^2 X^2 0 2X^2 0 2X^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 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 0 0 X^2 X^2 0 X^2 0 2X^2 2X^2 0 0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 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 2X^2 X^2 0 2X^2 2X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 2X^2 X^2 X^2 2X^2 0 2X^2 2X^2 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 X^2 2X^2 2X^2 X^2 2X^2 0 X^2 0 2X^2 0 2X^2 0 X^2 0 2X^2 0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 0 0 0 2X^2 X^2 0 X^2 2X^2 2X^2 0 0 X^2 2X^2 2X^2 2X^2 X^2 generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 120. Homogenous weight enumerator: w(x)=1x^0+28x^120+36x^121+144x^122+116x^123+324x^124+588x^125+456x^126+1296x^127+1740x^128+1928x^129+2502x^130+5472x^131+5152x^132+4074x^133+8268x^134+6538x^135+4956x^136+6306x^137+3564x^138+2040x^139+1920x^140+300x^141+732x^142+270x^143+30x^144+66x^145+54x^146+22x^147+12x^148+24x^149+34x^150+10x^153+18x^156+14x^159+8x^162+2x^165+4x^171 The gray image is a linear code over GF(3) with n=603, k=10 and d=360. This code was found by Heurico 1.16 in 10.2 seconds.