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 3 3 0 3 3 9 3 3 18 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 0 3 24 9 21 6 18 12 15 0 21 24 9 12 6 18 3 15 0 21 24 9 12 6 18 3 15 0 21 24 9 12 6 18 3 15 21 24 3 12 6 3 3 15 3 0 9 18 21 12 3 24 6 15 0 9 18 21 12 3 24 6 15 0 9 18 21 12 3 0 9 18 generates a code of length 72 over Z27 who´s minimum homogenous weight is 144. Homogenous weight enumerator: w(x)=1x^0+236x^144+2x^153+2x^162+2x^189 The gray image is a code over GF(3) with n=648, k=5 and d=432. This code was found by Heurico 1.16 in 0.129 seconds.