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 X X 1 1 1 1 1 0 1 X 1 1 1 1 1 X 1 1 1 X 0 X 1 1 X X X 0 1 X 1 1 0 X 2X 0 2X^2+X 2X 0 2X^2+X 2X X^2 2X^2+X 2X X^2+2X 0 2X^2+X X^2+X X^2+2X X^2 2X 0 2X^2+X X^2+X 0 2X X^2 X X^2+2X 2X^2+2X X^2 2X 0 2X^2+X 2X^2 2X X X X^2 2X^2+X 2X X^2+X 0 X^2+X 0 X^2 X X^2+2X 2X^2+X 2X^2+2X X^2+X 2X^2+2X X^2+X 2X^2 2X X^2+2X X^2 2X^2+2X 2X^2+X X 2X 2X^2+X 2X^2 2X^2+X 0 2X^2+X X 2X X^2+X 2X^2+2X 0 0 0 X^2 0 0 0 0 2X^2 X^2 0 X^2 2X^2 2X^2 0 0 X^2 0 0 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 0 2X^2 0 X^2 2X^2 2X^2 2X^2 0 2X^2 X^2 2X^2 0 0 2X^2 2X^2 X^2 X^2 0 2X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 0 2X^2 X^2 0 X^2 X^2 2X^2 2X^2 X^2 2X^2 0 0 X^2 X^2 X^2 0 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 0 2X^2 0 2X^2 0 0 0 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 0 2X^2 0 2X^2 X^2 X^2 2X^2 X^2 2X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 X^2 X^2 0 X^2 2X^2 0 2X^2 0 2X^2 0 2X^2 2X^2 0 0 2X^2 X^2 X^2 0 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 0 X^2 2X^2 X^2 0 2X^2 X^2 2X^2 0 0 X^2 2X^2 X^2 2X^2 X^2 2X^2 0 X^2 2X^2 0 2X^2 2X^2 X^2 X^2 0 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 0 0 2X^2 0 0 0 0 0 X^2 X^2 0 2X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 X^2 X^2 0 2X^2 0 0 2X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 2X^2 0 X^2 X^2 0 0 2X^2 X^2 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 0 0 0 0 X^2 0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 125. Homogenous weight enumerator: w(x)=1x^0+24x^125+238x^126+24x^127+150x^128+436x^129+138x^130+144x^131+1090x^132+234x^133+204x^134+3618x^135+294x^136+246x^137+5700x^138+282x^139+204x^140+4288x^141+252x^142+246x^143+896x^144+168x^145+144x^146+278x^147+66x^148+84x^149+108x^150+12x^152+58x^153+10x^156+10x^159+16x^162+2x^165+10x^168+6x^171+2x^177 The gray image is a linear code over GF(3) with n=621, k=9 and d=375. This code was found by Heurico 1.16 in 38.2 seconds.