The generator matrix 1 0 1 1 1 1 1 21 1 1 1 24 0 1 1 1 1 1 21 1 24 1 1 1 24 1 1 1 0 1 21 1 1 24 1 1 1 1 1 21 1 1 0 1 1 1 21 1 1 1 24 6 1 1 1 1 1 1 15 1 24 1 1 1 1 1 1 1 0 1 7 26 21 4 20 1 24 19 23 1 1 0 16 26 20 4 1 21 1 23 24 19 1 4 0 26 1 16 1 24 19 1 21 24 16 20 4 1 0 6 1 21 4 23 1 21 0 19 1 1 13 19 10 10 9 13 1 22 1 23 16 16 26 25 23 16 0 0 9 0 0 0 18 18 9 9 9 0 9 0 9 0 9 9 18 18 9 9 0 9 0 18 0 0 0 0 18 9 18 0 0 9 18 0 0 9 18 18 18 9 9 18 9 18 0 18 0 9 9 0 0 9 18 18 9 9 18 0 0 9 0 0 9 9 0 0 0 9 0 0 18 18 18 0 9 9 18 9 18 0 18 9 18 0 18 0 18 18 0 0 18 0 18 18 18 9 0 9 18 18 18 9 18 0 18 9 0 9 9 9 18 9 0 9 18 0 0 9 9 0 0 9 9 9 18 9 0 9 18 18 18 18 0 0 0 0 18 0 18 9 9 18 18 9 0 0 0 18 0 0 9 9 9 18 18 9 18 0 9 9 0 18 18 18 0 0 18 9 18 0 0 0 9 9 0 9 9 9 0 9 18 18 9 0 9 18 0 9 18 0 0 0 18 9 9 9 18 18 0 0 0 0 0 0 0 9 18 0 18 18 18 18 18 18 9 9 18 0 18 9 18 0 0 0 9 9 9 9 9 18 18 0 0 9 9 9 0 9 9 0 9 0 9 0 18 9 0 18 18 18 0 18 18 18 0 0 9 18 0 18 0 18 18 0 9 0 9 0 generates a code of length 68 over Z27 who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+94x^123+12x^124+96x^125+640x^126+162x^127+438x^128+2366x^129+738x^130+1662x^131+5268x^132+2160x^133+3840x^134+10030x^135+3714x^136+5154x^137+9820x^138+2760x^139+2868x^140+4916x^141+582x^142+438x^143+806x^144+66x^145+78x^146+154x^147+12x^148+6x^149+66x^150+42x^153+20x^156+22x^159+8x^162+6x^165+2x^168+2x^171 The gray image is a code over GF(3) with n=612, k=10 and d=369. This code was found by Heurico 1.16 in 11 seconds.