The generator matrix 1 0 0 0 1 1 1 18 1 1 1 1 1 15 12 1 1 3 1 1 1 1 1 9 1 1 1 1 1 1 1 3 1 6 12 1 15 24 1 1 24 3 1 1 1 15 1 9 1 1 1 1 1 3 1 9 24 1 0 1 1 1 1 1 18 1 1 15 1 0 1 0 0 18 1 19 1 18 0 26 23 22 24 1 12 2 1 12 10 7 8 14 1 2 3 14 23 16 22 21 1 6 1 1 23 1 15 13 23 3 1 11 11 11 1 3 1 4 3 0 25 18 3 23 21 1 5 1 24 18 5 22 25 1 20 12 9 0 0 0 1 0 16 25 14 7 4 23 12 13 11 1 5 20 8 18 0 22 6 10 6 13 24 17 8 1 11 15 1 25 12 24 2 5 26 1 21 20 1 13 21 20 9 11 22 14 13 5 9 5 12 1 25 3 18 3 9 7 4 1 5 20 21 10 24 1 9 0 0 0 1 14 9 5 5 22 24 1 6 16 23 2 5 13 4 20 7 17 2 2 1 0 16 26 10 6 13 18 21 4 20 25 3 12 19 15 21 7 14 2 13 25 19 6 15 10 26 10 22 23 17 17 1 6 17 19 10 25 15 23 7 8 0 12 1 0 generates a code of length 69 over Z27 who´s minimum homogenous weight is 126. Homogenous weight enumerator: w(x)=1x^0+364x^126+1044x^127+3522x^128+5618x^129+8424x^130+12348x^131+16864x^132+21624x^133+31566x^134+34858x^135+42126x^136+51012x^137+51386x^138+52362x^139+54768x^140+44456x^141+34518x^142+27936x^143+17038x^144+9840x^145+5412x^146+2396x^147+990x^148+462x^149+204x^150+90x^151+42x^152+44x^153+54x^154+30x^155+24x^156+12x^158+6x^159 The gray image is a code over GF(3) with n=621, k=12 and d=378. This code was found by Heurico 1.16 in 581 seconds.