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 1 1 2X^2+X 1 1 1 0 1 1 1 1 2X^2+X 1 2X 1 1 2X^2+X 0 1 1 1 2X 1 2X X^2+X 1 1 1 0 1 1 2X^2+X 1 1 1 1 1 1 1 1 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 X+1 2 2X^2+X 2X+2 1 2X^2+1 2X^2+X+2 0 1 2X^2+2X+1 2X X^2+2 2X^2+1 1 2X^2+X 1 2X 2X^2+2X+1 1 1 X+1 2X^2+X+2 X^2+X+2 1 X+1 1 1 2X^2+X+2 2 2 1 X^2+X 2 1 X^2+X+2 0 2X^2+X X+2 2X^2+1 2X X^2+2X X^2+2 2X^2+X+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 0 0 X^2 2X^2 0 X^2 X^2 2X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 2X^2 0 2X^2 0 0 X^2 X^2 0 0 X^2 2X^2 X^2 0 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 0 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 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 2X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 2X^2 X^2 0 2X^2 0 X^2 2X^2 2X^2 0 0 2X^2 X^2 0 X^2 X^2 X^2 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 0 X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 2X^2 X^2 0 X^2 X^2 0 2X^2 2X^2 X^2 X^2 X^2 2X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 2X^2 0 X^2 X^2 2X^2 0 0 0 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 X^2 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 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 0 0 X^2 0 0 2X^2 0 X^2 0 2X^2 2X^2 0 X^2 0 2X^2 2X^2 2X^2 0 0 0 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 0 2X^2 X^2 2X^2 0 0 X^2 2X^2 2X^2 0 2X^2 X^2 0 2X^2 2X^2 generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+130x^123+18x^124+18x^125+676x^126+342x^127+252x^128+2016x^129+1458x^130+1008x^131+5308x^132+3474x^133+2322x^134+9418x^135+6174x^136+3150x^137+9482x^138+4698x^139+1746x^140+4682x^141+1206x^142+252x^143+710x^144+126x^145+246x^147+64x^150+16x^153+18x^156+12x^159+6x^162+10x^165+8x^168+2x^177 The gray image is a linear code over GF(3) with n=612, k=10 and d=369. This code was found by Heurico 1.16 in 10.5 seconds.