The generator matrix 1 0 0 0 1 1 1 2X^2 1 1 1 1 1 2X 1 1 1 X 2X^2+X X 1 1 1 0 1 1 1 2X^2+X X 1 1 1 1 X^2+X 1 1 1 2X^2+X 1 1 2X^2 2X 1 1 1 2X^2+2X 1 1 1 X^2+X X 2X^2+2X 2X^2+2X 1 X 1 1 2X^2+X 1 1 1 2X 1 1 1 1 1 1 1 1 0 X^2+2X 1 0 1 0 0 2X^2 1 X^2+1 1 X X^2+X 2X^2+2X+2 X^2+2 X^2+X+1 1 X^2+2 2X^2+2X+1 X^2+2X+2 1 1 2X^2+2X X^2+2X X^2 1 2X^2+2X X+1 2X^2+2 2X+2 1 1 X^2 X+2 2X 2X+1 1 X^2+X+1 X^2+X+2 2 X 2X X^2+2X+1 1 1 X^2+X 2X^2+1 2X 1 2X+1 X^2+2X X+2 1 2X 1 X^2 2X^2+X+1 1 X^2+X X^2+X+2 1 2X^2+1 0 X^2+2 1 X^2+X+1 X^2+2X 2X^2+X 1 2X+1 X^2+2X+1 2X^2+2X+1 X+2 X^2 1 2X^2 0 0 1 0 2X^2+2X+1 2X+1 2X^2+X+2 2X^2+2X+1 X+1 X+2 2X^2 2X^2+X+1 2X^2+X+2 2X+2 X^2+2 X^2+2X+1 X^2+X 2X^2+2 2X^2 1 2X^2+2X 2X^2+X+1 0 1 X^2+2X 2X^2+2X+2 X^2+1 2X^2+X+1 2X X^2+X 2X X^2+X+2 2X+2 X+1 X^2+X+1 X^2+2X+2 X^2+2X+1 1 2 2X^2 X^2+2X+1 2X^2+2X+2 X^2+X+2 X^2+1 2X^2+2X+1 X+1 2X^2+2 X 2 2X 1 1 X^2+2X 2X^2+X+1 2X+2 X^2+2X+2 2X^2 2X^2+X+2 2X^2+2X+2 2 2X^2+2X+1 2X^2+X 2X^2+2X 2X^2+X+2 X X^2+X+1 X^2+1 2X^2+2X 2X+2 X^2+X+1 1 2X+1 2X 0 0 0 1 2X^2+2X+2 X^2 X^2+2X+2 X^2+2X+2 1 X^2+X 2X^2+1 2X^2+2X 2X^2+2X+1 0 2X^2 2X^2+2 X^2+X+2 2X^2+2X+2 2X^2+2 X^2+2 1 X^2+X 2X 2X^2+2X+1 X^2+2 X+2 2X+2 2X^2+X+1 2X+1 2X^2+2 2X X^2+2X+1 0 X 2X^2+X+1 X^2+1 2X+1 X^2+2 2X+2 X^2+2X+1 2X^2+2 X^2+1 2X^2+X+1 X^2+2 2X^2+X X+1 2X+2 2X^2+2X+1 2X+1 2X^2+2X X^2+X+1 X 1 2X 2X^2 X^2+2 1 X^2+2X+2 2X^2+X+1 1 2X^2+X+2 X+1 2X^2+2X+2 X^2 X^2+X 2 X+2 X^2+X+2 X+1 X^2+X 2X^2+X 2X^2+X X generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 134. Homogenous weight enumerator: w(x)=1x^0+564x^134+1466x^135+3192x^136+6246x^137+8800x^138+13788x^139+18594x^140+21536x^141+29484x^142+38646x^143+38520x^144+47730x^145+54360x^146+47212x^147+51018x^148+48216x^149+34078x^150+26424x^151+19122x^152+10618x^153+6588x^154+2970x^155+1186x^156+516x^157+264x^158+102x^159+90x^160+42x^161+14x^162+18x^163+18x^164+12x^167+6x^168 The gray image is a linear code over GF(3) with n=657, k=12 and d=402. This code was found by Heurico 1.16 in 591 seconds.