The generator matrix 1 0 0 1 1 1 1 1 1 X 1 1 X^2 1 1 2X^2+X 1 1 2X^2+X 1 1 2X^2 2X^2+2X 1 1 1 1 1 1 0 X^2 2X^2+2X 1 1 1 1 1 1 1 0 X^2+X 1 1 1 1 1 1 X^2+2X 1 1 1 1 1 2X 1 1 1 X^2+X 1 1 X 1 0 1 1 X 1 1 1 1 1 1 1 1 1 2X^2+2X 1 1 0 1 0 0 X^2 2X^2+2X+1 2X^2+2 2 X+2 1 1 X^2+2X+1 1 2X^2+X 2X^2+2X+2 1 2X^2+2X+2 2X^2+2X+1 1 2X^2+2X 2X^2+1 1 X^2+X X^2+X+2 X X^2+1 X^2+2X+1 X^2+2X X^2 X 1 1 2X+2 2X+2 1 2 X^2+X 2X+1 X^2+2X+2 1 2X^2 X^2+2X+2 X^2+X X^2+2X X^2+X+1 X^2+2 2X^2+2X+2 1 X^2+X+2 2X 2X^2+1 X^2+2X+1 2X^2+2X 1 0 2X X^2+X 1 X^2+X+2 X^2+2 1 2X^2+X+2 1 2X X^2+2 2X^2+2X X^2+1 X^2+2X+1 X^2+X 2X^2+1 2X^2+2X+2 2X^2+X+2 2X^2+X+2 X+1 X^2+1 1 2X^2+X+2 0 0 0 1 2X^2+2X+1 2X^2+2 X^2+2 2X^2+X+2 X^2 1 2X+1 X^2+2X+1 2X 2X^2+2 2X^2+2X X^2+2X+1 2X^2+2 2X^2+X X^2+X+1 2X^2+X+1 2X^2+2X+1 X^2+2X 2X^2+X 1 2X^2+2 X^2+X+2 X^2+2 2X^2+2X+2 X^2+2 2X 1 2X^2+X+2 2X^2+X+1 1 X^2+2X+2 X^2 X 2X^2+2X+2 2X^2+1 2X^2+2 2X 1 2X^2 2X+1 2X^2+1 X^2+2X+1 2X^2+2 X^2+2X 0 X^2+2X+1 2X^2+X+2 X^2+X+2 2X+1 2X^2+1 1 1 2X^2+X+2 X^2+X 2X^2 2X^2+X 2X^2+X+1 2X^2+X+2 2X^2+X+2 X^2+X X^2+2 2X^2 1 2X^2+X X^2+2X 2X^2+1 2X^2+2X+1 X^2+X+2 2X^2 2X+1 X X^2+1 2 2X^2+X+2 X^2 0 0 0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 X^2 2X^2 0 X^2 X^2 X^2 X^2 2X^2 2X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 2X^2 0 2X^2 0 X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2 0 0 0 0 X^2 X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 2X^2 2X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 147. Homogenous weight enumerator: w(x)=1x^0+292x^147+600x^148+2124x^149+2658x^150+2754x^151+4350x^152+5326x^153+3816x^154+5712x^155+5654x^156+4116x^157+5058x^158+4568x^159+2904x^160+3240x^161+2530x^162+1128x^163+1266x^164+518x^165+180x^166+72x^167+52x^168+30x^169+24x^170+6x^171+24x^172+24x^173+10x^174+6x^177+6x^180 The gray image is a linear code over GF(3) with n=702, k=10 and d=441. This code was found by Heurico 1.16 in 9.53 seconds.