The generator matrix 1 0 0 1 1 1 1 1 1 1 2X^2+2X 1 X^2 1 1 2X^2+X 0 X^2 1 1 2X 1 1 1 1 1 1 1 1 1 2X^2+X 1 1 1 0 X^2+X 1 1 2X^2+2X 2X X 1 1 1 2X^2+2X 1 1 1 1 1 1 X X^2+X 1 1 1 1 2X X 1 X^2+2X 1 0 2X 1 1 1 1 1 2X^2 1 1 1 1 1 1 2X^2+2X 0 1 0 1 0 0 X^2 2X^2+2X+1 2X^2+2 2 2X^2+2X+2 2X^2+X+1 1 X^2+2X+1 1 2X^2+X X+2 1 1 1 2X^2+2X+2 X^2 2X^2+X 2X^2+X+2 X^2+2X+1 2X^2+2X+1 X^2+2X 2X^2+X+1 2X^2+X+2 X^2+X+1 2X^2+1 X^2+X 2X^2 2X^2+2 X+1 X^2+X 1 1 2X^2+2X 2 1 1 2X^2+X 2 X^2+X+1 2X^2+X+1 X^2 X^2+1 X^2+X X^2+X+2 2X^2+1 2X^2+2 X^2 1 1 2X^2+X X^2+X 2X^2+1 X^2+2X+2 1 1 2X^2+2X+2 1 2X^2+2X 1 1 2X^2+1 2X 2X^2 X^2+2X X^2+X+2 1 X^2+X+2 X^2+X X^2+X+1 1 0 2X+2 2X^2+X X^2 0 0 0 1 2X^2+2X+1 2X^2+2 X^2+2 2X^2+X+2 X^2 X^2+2X+1 2X^2+1 X^2+2X+1 0 2X^2+2 X^2+2X X^2+1 2 2X 2X+1 X^2+X+2 2X^2+X+2 1 X^2 2X 1 2X^2+2X+1 X^2+2 2X^2+X+1 X^2+2X+1 2X 2 1 X^2+2X+2 X+2 X^2+1 X+2 X^2+2X+1 2X^2+2X X^2+2X 2X 2X^2+X+1 1 2X+1 X+2 X^2+X+1 1 2X^2 1 2X^2+X+2 X^2+2X+2 2X^2+X 0 2X^2+X+2 1 2X^2+X+2 2X+1 2X^2+X+1 X+1 X^2+2X X^2+X 2X 2X^2+2X+2 2X^2 X^2+X 0 2X^2+2 X+2 X^2+X+2 2X^2+X+1 2X^2+X+2 2X^2+1 2X^2+2X+1 2X+2 X^2 X^2+1 X 2X^2+2 1 1 2X^2 0 0 0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 2X^2 0 0 0 X^2 X^2 0 X^2 X^2 2X^2 0 0 X^2 2X^2 2X^2 0 2X^2 0 2X^2 0 X^2 0 0 0 2X^2 X^2 X^2 0 X^2 0 2X^2 X^2 0 X^2 2X^2 2X^2 2X^2 0 X^2 X^2 0 0 2X^2 0 2X^2 X^2 2X^2 X^2 2X^2 generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 149. Homogenous weight enumerator: w(x)=1x^0+384x^149+880x^150+1446x^151+3186x^152+3684x^153+3264x^154+4698x^155+5178x^156+4458x^157+5094x^158+5466x^159+3936x^160+4692x^161+4030x^162+2616x^163+2574x^164+1618x^165+762x^166+684x^167+248x^168+12x^169+42x^170+20x^171+24x^172+18x^173+8x^174+12x^176+6x^178+2x^180+6x^183 The gray image is a linear code over GF(3) with n=711, k=10 and d=447. This code was found by Heurico 1.16 in 9.28 seconds.