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 1 1 1 X 1 1 0 1 X 1 1 1 1 1 1 X 1 1 0 1 0 1 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+2X X 0 X^2+2X 2X^2+X 2X^2 X^2+X 2X^2+2X X^2 2X X^2+X X X^2 2X^2+X 2X^2+2X 2X^2 X^2+X 2X 2X^2+2X X X 2X^2+X 2X^2+X 2X^2+2X X^2+2X 2X 2X^2 X^2 X^2+2X 2X X^2 X^2+2X X X^2 X 2X X^2+2X 2X^2+X 0 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 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 0 2X^2 0 2X^2 2X^2 0 2X^2 X^2 0 2X^2 2X^2 0 2X^2 2X^2 X^2 X^2 2X^2 0 0 X^2 0 0 0 2X^2 0 X^2 X^2 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 2X^2 0 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 0 2X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^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 0 0 2X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 2X^2 2X^2 X^2 2X^2 0 0 X^2 0 2X^2 0 0 X^2 X^2 2X^2 2X^2 0 0 X^2 2X^2 0 2X^2 X^2 0 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 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 X^2 0 2X^2 0 0 2X^2 X^2 X^2 2X^2 2X^2 X^2 0 2X^2 X^2 2X^2 0 X^2 0 2X^2 0 X^2 0 2X^2 0 0 2X^2 2X^2 2X^2 0 X^2 2X^2 0 generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 114. Homogenous weight enumerator: w(x)=1x^0+44x^114+72x^116+226x^117+24x^118+168x^119+508x^120+102x^121+468x^122+422x^123+732x^124+2142x^125+622x^126+2376x^127+4164x^128+496x^129+2328x^130+2808x^131+524x^132+186x^133+162x^134+388x^135+84x^136+150x^137+234x^138+72x^140+90x^141+36x^144+20x^147+14x^150+12x^153+2x^156+2x^159+2x^162+2x^168 The gray image is a linear code over GF(3) with n=576, k=9 and d=342. This code was found by Heurico 1.16 in 2.28 seconds.