The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 0 1 1 1 3 1 3 1 1 0 3 24 0 21 24 0 21 24 9 21 24 12 6 0 12 0 21 24 24 18 15 21 24 15 3 21 21 0 21 9 21 12 0 0 0 9 0 0 0 0 18 9 0 9 18 9 0 0 9 9 18 18 18 18 9 0 9 0 0 9 0 18 0 9 18 18 18 0 0 0 9 0 0 0 0 0 18 9 18 18 18 9 18 0 18 9 0 9 0 18 9 0 18 18 18 0 18 9 18 0 18 0 0 0 0 18 0 9 18 9 9 18 18 18 18 0 0 0 9 18 0 9 9 18 18 9 0 9 0 9 18 9 0 9 18 0 0 0 0 0 9 9 0 18 9 9 9 18 0 9 18 9 18 9 18 18 9 0 0 9 18 9 9 9 18 0 18 18 9 generates a code of length 34 over Z27 who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+120x^57+72x^59+310x^60+72x^61+330x^62+494x^63+252x^64+1230x^65+3642x^66+432x^67+2328x^68+6650x^69+522x^70+1668x^71+710x^72+180x^73+174x^74+306x^75+30x^77+86x^78+40x^81+18x^84+10x^87+6x^90 The gray image is a code over GF(3) with n=306, k=9 and d=171. This code was found by Heurico 1.16 in 1.03 seconds.