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 1 X X X 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 2X^2 0 2X^2 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 X^2 X^2 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 2X^2 0 0 2X^2 0 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 X^2 0 X^2 0 0 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 2X^2 X^2 X^2 X^2 X^2 generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 126. Homogenous weight enumerator: w(x)=1x^0+102x^126+6x^127+86x^129+66x^130+118x^132+192x^133+92x^135+342x^136+4442x^138+474x^139+52x^141+294x^142+54x^144+84x^145+26x^147+30x^150+32x^153+26x^156+12x^159+14x^162+8x^165+2x^168+2x^171+2x^174+2x^186 The gray image is a linear code over GF(3) with n=621, k=8 and d=378. This code was found by Heurico 1.16 in 0.583 seconds.