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 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 X 1 1 1 1 1 1 1 1 1 X 1 1 1 X X X 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X 2X X X X 0 X X X 2X 0 0 2X X X 2X 0 2X X 0 X X 2X 0 0 0 2X X 0 2X X 0 0 0 X X 2X X 0 X 0 2X 0 2X 2X X 0 X X X X 2X X 2X 0 X 2X 0 2X X X X 2X 0 X X 0 0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X 2X 0 X X 2X 2X 2X 2X 2X 2X X 2X 0 X 2X 0 2X 0 X X 0 2X 0 X 0 X 0 X X 2X 0 0 X 2X X X 0 0 0 2X 0 0 X 2X 2X 2X 2X 2X 2X 0 X X X X 2X 2X 2X X 2X X 0 X 0 0 0 X 0 0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 X X 0 2X X 0 0 0 X X X 2X 2X 2X 0 X 0 2X 0 2X 0 2X X 0 X 0 X X 2X 2X 0 0 X 0 0 X X 2X 2X X 2X 2X 0 X 2X 0 X X 0 X 2X 0 0 X X 0 0 0 2X X 2X X X 0 2X 0 0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X X 0 0 0 X 0 0 2X X X X 0 0 2X 0 2X 2X 0 2X 2X X X 2X X 0 X 2X X 0 2X 2X X X X 0 2X 0 0 0 0 2X 2X 0 X 0 0 2X X 2X 0 2X 2X 0 0 X X X X X 0 2X 2X X 2X 0 0 0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 2X X X 2X 2X X 0 0 2X 2X 2X 2X 0 0 2X X 0 0 2X 2X X 2X 0 X X 2X X 0 0 2X 2X 0 X X X 0 X X 0 X 2X 0 0 0 0 X X 0 0 0 2X X X 2X 0 X 2X 0 2X 0 X 2X X X X 0 0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X X X X X 2X 0 0 X 2X 0 X 2X 2X X X 2X 2X X 0 2X X 0 X 0 0 X 2X X X X X 0 X X 0 2X 2X 0 2X 2X 0 0 0 2X 0 2X X 0 0 0 0 X 2X 2X 2X X 2X 2X 2X X 2X 2X X 2X 0 X generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 159. Homogenous weight enumerator: w(x)=1x^0+62x^159+166x^162+238x^165+324x^168+510x^171+888x^174+1454x^177+1272x^180+822x^183+306x^186+112x^189+88x^192+72x^195+86x^198+50x^201+42x^204+38x^207+20x^210+6x^213+2x^222+2x^243 The gray image is a linear code over GF(3) with n=267, k=8 and d=159. This code was found by Heurico 1.16 in 1.95 seconds.