The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X 1 1 X X X 1 1 1 1 1 X X 1 1 1 1 1 1 X X 1 1 1 1 1 1 1 1 1 1 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 2X X 2X X X 2X 0 X 0 0 X X 2X 2X 2X 2X X 2X 2X X X X 2X X X 0 X 0 0 2X 0 0 2X 0 0 X X 0 X 0 X X X X 0 X 0 X X 0 X X 2X 2X 0 2X X 2X X 0 2X 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X 2X 2X 0 2X X 0 2X 0 2X 0 X 0 X 2X 2X X 2X X 2X 2X 2X X 2X 0 2X X 2X X 0 0 X 2X 0 X X X 0 X X 2X X 0 X 0 X 2X 0 X 0 2X X 2X 0 0 0 2X X X X X X 0 0 0 0 0 X 0 0 0 0 0 X X 2X 2X 2X 0 2X 0 0 X 2X 2X 2X X X 2X 0 2X X 2X 2X 0 2X 2X 2X X X 0 X 2X X 2X 0 X 2X X X X 2X X 2X X X X X X 0 2X X 2X 2X X X 0 X X 0 0 0 2X 0 0 X 0 2X 2X X 0 0 0 0 0 X 0 0 0 X 2X 2X 2X X X 2X 2X X 0 X X 2X 2X X 2X 0 X 0 0 0 2X 0 X X 0 2X 0 X X 2X 2X 0 2X X X 2X X 2X 0 X 2X 2X 0 2X 2X 2X 0 2X X 0 0 2X X X 2X 2X 2X 0 X X X 0 X X 2X 2X X 0 0 0 0 0 0 X 0 0 2X 2X X X 0 2X 0 X X 2X X 0 0 2X X 2X X X 0 X 0 X X X 0 2X 2X X 0 2X 2X 0 0 2X 0 X X 2X 2X 0 2X 0 0 X X 2X X X 0 0 2X 2X X 2X 2X 0 2X 2X 0 2X 2X X X 0 2X 0 2X 0 0 0 0 0 0 0 0 X 0 2X X 2X X 2X 0 0 0 0 X 2X 2X 0 0 2X 0 X X 0 X 0 0 2X X X 2X 2X X 2X 2X X 0 2X 0 X 0 2X X X 2X 2X X 2X 0 X X 0 X X 0 2X 0 X 2X 0 0 X 0 2X 0 0 0 2X 2X 2X 2X X 2X 0 0 0 0 0 0 0 0 X X 0 X 0 X 0 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X X 0 0 X X 2X 2X X 0 2X X X 0 X 2X X X 0 0 0 X 2X 0 2X 0 0 0 2X X X 2X X 2X 2X 0 2X 0 2X 2X 2X 0 2X X 0 2X X X X X X 2X X generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 129. Homogenous weight enumerator: w(x)=1x^0+44x^129+166x^132+354x^135+342x^138+30x^140+478x^141+264x^143+458x^144+696x^146+506x^147+1830x^149+524x^150+2928x^152+554x^153+3468x^155+536x^156+2514x^158+490x^159+1182x^161+484x^162+210x^164+476x^165+354x^168+302x^171+216x^174+134x^177+86x^180+36x^183+14x^186+2x^189+2x^192+2x^201 The gray image is a linear code over GF(3) with n=231, k=9 and d=129. This code was found by Heurico 1.16 in 14.6 seconds.