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 X X 1 X 1 1 1 1 X 1 X X 1 1 1 1 1 0 X^2 0 0 0 0 0 0 0 0 X^2 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 X^2 0 X^2 0 2X^2 X^2 0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 0 X^2 2X^2 2X^2 0 0 0 X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 0 X^2 2X^2 2X^2 X^2 X^2 0 X^2 X^2 2X^2 X^2 0 0 X^2 X^2 0 0 2X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 2X^2 2X^2 2X^2 0 0 2X^2 X^2 2X^2 X^2 0 X^2 X^2 0 2X^2 2X^2 0 X^2 X^2 2X^2 0 X^2 0 2X^2 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 2X^2 0 2X^2 0 0 2X^2 X^2 X^2 2X^2 0 X^2 0 2X^2 0 2X^2 2X^2 0 2X^2 0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 0 2X^2 X^2 0 2X^2 X^2 2X^2 2X^2 X^2 X^2 0 X^2 X^2 0 0 0 2X^2 X^2 2X^2 0 X^2 0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 X^2 0 2X^2 2X^2 0 X^2 2X^2 0 2X^2 X^2 0 X^2 0 X^2 0 2X^2 2X^2 0 0 2X^2 2X^2 X^2 0 X^2 2X^2 X^2 0 X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 0 X^2 X^2 2X^2 0 X^2 X^2 X^2 0 0 X^2 2X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 X^2 0 0 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 2X^2 X^2 2X^2 0 0 X^2 X^2 0 2X^2 0 0 2X^2 X^2 2X^2 0 X^2 0 2X^2 0 0 2X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 129. Homogenous weight enumerator: w(x)=1x^0+54x^129+100x^132+36x^133+120x^135+90x^136+86x^138+360x^139+98x^141+4824x^142+60x^144+396x^145+32x^147+126x^148+34x^150+36x^153+30x^156+26x^159+20x^162+10x^165+8x^168+6x^171+4x^174+2x^177+2x^195 The gray image is a linear code over GF(3) with n=639, k=8 and d=387. This code was found by Heurico 1.16 in 0.534 seconds.