The generator matrix 1 0 1 1 1 1 1 1 2X^2+X 2X 1 1 1 1 0 1 1 2X^2+X 1 1 1 1 1 1 2X X 1 2X^2 1 1 1 1 1 0 2X^2+X 1 1 1 1 1 1 1 1 1 X^2 1 2X 1 2X^2+2X 1 1 1 1 1 1 1 2X 1 2X^2+X 1 1 0 1 1 1 0 X 1 1 2X^2+2X 1 1 X 1 0 1 1 2 2X^2+X 2X 2X^2+X+2 2X+2 1 1 2X^2+2X+1 X+1 2X^2 2X^2+2 1 2X+1 X 1 2X^2+X+2 1 2X^2+2X 2X+2 2 2X^2+X+1 1 1 X 1 2X^2+X+1 X+2 2X^2 2 0 1 1 X+1 2X+2 2X 2X^2+2X+1 X^2+2X+2 2X^2+1 2 1 X^2+2X 1 X+1 1 X^2+2 1 X+2 2X^2+2X+1 X^2 X X^2+2X+1 X^2+2X X^2+X+2 1 2X+1 1 X^2+1 X^2+2X+1 1 X^2+X 2X+2 X 1 2X^2+2X 2X 2X^2+2 1 1 X^2 2X 2X^2+2 0 0 2X 0 0 X^2 2X^2 0 X^2 X^2 2X^2+2X 2X 2X^2+X X 2X X X^2+X 2X^2+2X 2X^2+2X X^2+X X X^2+2X X^2+2X X^2+X 2X^2+2X X X X X^2+X 2X^2+X X 2X 2X 2X^2+2X X^2 0 2X^2+2X X^2 2X 2X^2 0 X^2+2X X^2+X 2X^2 0 2X^2+2X X^2 2X^2+X 2X^2+X X^2 X^2 X^2+2X X^2+2X 2X^2+2X 2X 2X^2 2X^2+2X 2X^2+X 0 X^2+X 0 0 2X^2 2X^2+X X^2 X^2+2X X^2+2X 2X 2X^2+X 2X^2+2X X^2+2X 2X^2+X 2X^2+X X^2 0 0 0 X^2 0 0 0 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 0 X^2 2X^2 X^2 2X^2 2X^2 0 X^2 0 0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2 0 2X^2 0 0 0 0 0 2X^2 0 0 2X^2 2X^2 X^2 2X^2 0 0 X^2 2X^2 0 2X^2 X^2 2X^2 2X^2 X^2 0 2X^2 0 X^2 2X^2 0 2X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 2X^2 X^2 X^2 2X^2 X^2 2X^2 0 0 0 0 2X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 0 2X^2 2X^2 0 X^2 X^2 0 0 2X^2 2X^2 2X^2 X^2 0 2X^2 X^2 2X^2 X^2 2X^2 2X^2 0 0 0 X^2 2X^2 0 2X^2 X^2 0 X^2 2X^2 0 X^2 0 X^2 2X^2 0 X^2 2X^2 2X^2 2X^2 0 X^2 X^2 0 0 0 X^2 0 2X^2 X^2 0 2X^2 generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 138. Homogenous weight enumerator: w(x)=1x^0+660x^138+180x^139+648x^140+2270x^141+1944x^142+2682x^143+4326x^144+3474x^145+4104x^146+5676x^147+5724x^148+5418x^149+6132x^150+4482x^151+3744x^152+3386x^153+1656x^154+864x^155+960x^156+36x^157+36x^158+274x^159+246x^162+102x^165+14x^168+4x^171+4x^177+2x^180 The gray image is a linear code over GF(3) with n=666, k=10 and d=414. This code was found by Heurico 1.16 in 57 seconds.