The generator matrix 1 0 0 1 1 1 1 1 0 2X 1 1 1 1 1 1 0 1 1 1 1 0 2X 1 1 2X 1 1 0 1 1 2X 1 1 0 X 1 0 1 2X 1 1 1 1 X 1 1 X 2X 1 1 1 1 X X 1 1 1 1 1 1 0 2X 1 X 1 1 1 1 1 2X 1 1 1 0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2X 1 2X+1 2X 2 0 X+2 1 1 1 0 2 1 0 2 1 X+2 2X+1 1 2X+2 X+1 X 1 2X 0 2X+1 1 1 X+1 X+2 X 1 2X 0 1 1 1 X X 2X+2 1 1 2 X+2 2 2 1 2X 1 1 0 1 1 X 2X X+2 1 1 2X+1 X 0 0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 2X+1 1 2X+2 1 X+1 2X+2 2X+2 0 1 X 2X 2X X+2 X+1 2X+1 X 0 2 1 X+2 1 1 X+2 X 1 2X+1 X+1 2 2X X+1 X+2 2 2X X+2 1 X+2 X+2 X+2 1 2X+2 X X 2X+2 2X 2X 1 2X+1 2X+1 X 0 X+1 1 2X X 2X+1 2X+1 X 2X+1 2 X+1 0 0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 X 0 2X 0 X 2X 2X 2X 2X 2X X 2X 2X 2X 0 X 2X 2X 2X X 2X 0 2X X 0 2X 2X 2X X 2X 2X X 0 2X 0 0 X 2X X 0 X X 0 2X X 2X 2X X 0 2X 0 2X X 0 0 0 X 2X X 0 0 0 0 2X 0 0 0 0 0 X 2X 0 2X 0 0 0 0 X 0 X 2X 2X 2X 2X X X X X X X 2X 0 X X X X 2X 0 2X 2X 0 0 0 0 2X X 2X 0 X X X X X 2X X 0 X X 2X X X 0 2X X X 0 X 2X X X X X 2X 0 0 0 0 0 X 0 X X 2X X 2X 2X 2X X 2X X 0 2X 2X 0 2X 0 0 2X 2X X 2X X X 2X X 0 2X 2X 2X 0 2X 0 X 2X X X X 0 0 2X X X X 0 2X 0 2X X 2X X X X X 2X X 0 0 2X X 0 X 2X 0 X X 2X 2X 0 0 0 0 0 0 X X X X 0 0 2X X 0 0 2X X 2X 2X 2X X 0 0 0 2X 2X X 2X 2X X 0 2X 2X 2X 2X 0 0 2X X 0 X 2X X X 2X 2X 2X 0 0 2X 0 2X X 0 2X 2X 0 0 2X 2X X X 2X X X X X X 0 2X 0 0 0 generates a code of length 74 over Z3[X]/(X^2) who´s minimum homogenous weight is 129. Homogenous weight enumerator: w(x)=1x^0+106x^129+898x^132+2282x^135+3912x^138+5958x^141+7936x^144+9152x^147+9784x^150+8582x^153+5768x^156+2968x^159+1176x^162+312x^165+132x^168+26x^171+22x^174+20x^177+4x^180+6x^183+4x^186 The gray image is a linear code over GF(3) with n=222, k=10 and d=129. This code was found by Heurico 1.16 in 58 seconds.