The generator matrix 1 0 0 0 1 1 1 1 1 X 1 1 1 1 1 1 X 0 1 1 1 1 1 2X 2X 1 1 1 1 0 1 1 0 0 1 0 1 2X 1 1 1 X 1 0 1 1 1 0 1 1 1 2X 1 2X 1 1 2X X 1 1 1 1 1 2X 1 1 1 1 1 1 1 0 0 1 0 1 1 1 X 1 1 1 1 0 1 0 0 0 0 2X 2X+1 X+1 1 X 2 X+2 2 1 X+2 1 1 1 X 0 X+2 X+2 1 1 X+1 X+1 2X+2 2 1 2X X+1 1 0 2X 1 2 1 X+1 2X 2 1 1 2X 2X+1 X+2 X+2 0 X+1 2X X 1 2 1 1 X 0 0 0 X 2X+1 X+1 2X+2 1 X 2X+1 X+1 1 X+2 0 2 1 1 1 1 2X 1 1 1 X+2 2X+1 2 0 0 0 1 0 0 0 2X+1 X+1 2 X+1 1 X 2X+1 2 X 1 X+1 2X+2 X+2 X+2 X+2 1 X 2X+1 0 0 X+2 2 2X 0 2 X+1 X+2 1 2X X+1 X+2 2 2 1 2 X+1 X 1 2X X 2 1 1 X+2 2X X X 2X+2 2X 0 1 1 1 2X+2 X+1 2X+2 X X 2X X+2 X+2 2X+2 X+1 2X+1 2X+2 X+1 1 X+1 X 1 X+2 0 0 X 2X+1 X+2 X+1 0 0 0 1 1 2 2X+2 X+1 X+2 1 X 0 X+1 2 2X X 0 2X+2 X+1 1 X 2X+2 2 2X+2 2X+1 2X+2 X 1 X+1 2 2X+2 2X 2X+1 2X+1 2X+2 2X 0 2X X+1 1 X 2 2 0 0 2X X+1 X+1 1 2X+2 X X+2 1 X 2X+1 X+1 2 2X+2 2X+1 0 2X+1 X 1 2X 2X+1 2X 1 X+2 X+1 X+2 2X+2 2 X+2 2 2 X+1 2 2 1 1 0 2X+1 X+1 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 X X X X 2X 0 2X X 2X X 2X 0 2X 0 2X 2X X 2X X 2X 0 X 2X X X X 0 0 0 2X X X 2X 2X 0 X 0 X 0 0 X 2X 0 X X 2X 2X 2X X X 2X 0 0 2X 0 X 2X 2X 2X X 0 0 X 0 X 2X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X 2X 2X 2X X 2X X 0 2X 0 2X X X 2X 2X 2X 2X 2X 2X 0 0 X X 0 X 2X X 2X 2X X X 0 0 X X 2X 0 0 X 0 2X 0 2X 0 2X X X X X 0 0 X 2X 0 2X X X 2X X X 0 0 2X 2X 2X X 2X 2X 2X X X generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 149. Homogenous weight enumerator: w(x)=1x^0+348x^149+334x^150+1470x^152+908x^153+2658x^155+1644x^156+3624x^158+2092x^159+4656x^161+2426x^162+5400x^164+2814x^165+6066x^167+2814x^168+5760x^170+2666x^171+4560x^173+2006x^174+2622x^176+1092x^177+1446x^179+582x^180+552x^182+226x^183+192x^185+32x^186+6x^188+20x^189+6x^191+4x^192+6x^195+12x^198+2x^201+2x^204 The gray image is a linear code over GF(3) with n=249, k=10 and d=149. This code was found by Heurico 1.16 in 68.6 seconds.