The generator matrix 1 0 1 1 1 1 1 2X^2+X 1 2X 1 1 1 1 0 1 1 2X^2+X 1 1 2X 1 1 1 1 1 2X 2X^2+X 1 1 0 1 1 1 1 2X^2+X 2X 0 1 1 X^2+X 1 2X^2+X 1 2X^2+X 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 X^2+X 2X 1 1 0 1 2X^2+2X+1 2 2X^2+X X+1 2X^2+X+2 1 2X^2+1 1 2X 2X+2 2 0 1 2X^2+2X+1 2X^2+X+2 1 X+1 2X^2+X 1 2X^2+1 2X 2X+2 2 2X^2+1 1 1 2X+2 2X^2+2X+1 1 2X 2X^2+X 2X^2+1 2 1 1 1 0 2X^2+X 1 X+1 1 2X^2+1 1 2X+2 2X^2+2X+1 X+1 2X^2+2X+1 X^2+2X+1 0 X^2 2X+2 2 0 2X^2+X+2 1 X^2+1 2X^2+X+2 2X^2+X 1 1 2 0 0 0 2X^2 0 0 0 2X^2 2X^2 X^2 2X^2 2X^2 0 X^2 0 X^2 X^2 X^2 0 2X^2 X^2 2X^2 0 X^2 X^2 2X^2 0 X^2 X^2 0 0 X^2 2X^2 X^2 0 0 2X^2 2X^2 0 X^2 2X^2 X^2 0 2X^2 0 2X^2 0 2X^2 X^2 X^2 0 X^2 0 0 X^2 0 2X^2 0 X^2 2X^2 2X^2 0 2X^2 0 0 0 0 0 X^2 0 0 2X^2 2X^2 0 X^2 0 X^2 0 X^2 2X^2 2X^2 0 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 0 2X^2 0 X^2 2X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 2X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 2X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 0 0 0 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 X^2 0 2X^2 0 0 2X^2 0 0 2X^2 X^2 0 0 0 0 0 X^2 X^2 2X^2 0 2X^2 X^2 0 2X^2 2X^2 2X^2 0 X^2 0 2X^2 0 0 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 2X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 0 X^2 0 2X^2 0 0 2X^2 X^2 0 2X^2 0 X^2 0 2X^2 X^2 0 2X^2 2X^2 0 X^2 0 2X^2 X^2 X^2 2X^2 0 0 0 2X^2 X^2 0 X^2 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+34x^114+144x^116+192x^117+144x^118+636x^119+560x^120+1098x^121+1638x^122+1658x^123+3582x^124+4548x^125+4044x^126+6804x^127+7272x^128+5216x^129+7164x^130+5448x^131+2862x^132+2898x^133+1788x^134+508x^135+180x^136+300x^137+124x^138+96x^140+18x^141+22x^144+38x^147+14x^150+10x^153+2x^156+4x^159+2x^162 The gray image is a linear code over GF(3) with n=576, k=10 and d=342. This code was found by Heurico 1.16 in 9.65 seconds.