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 X X 1 X 1 X 1 1 X X 1 X X X X X X X X 1 1 1 1 1 X X X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 2 2 X^2 2 2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 2 X^2 2 X^2 2 X^2 2 X^2 0 X^2+2 0 X^2+2 0 X^2+2 X^2+2 X^2+2 0 X^2+2 X^2+2 X^2+2 2 2 0 0 2 0 X^2 X^2 2 X^2 2 X^2 2 X^2 X^2 X^2 2 X^2 0 2 X^2+2 X^2 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 2 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 0 2 2 0 2 2 2 2 2 2 0 0 2 2 2 0 2 0 0 2 2 0 0 0 0 0 0 0 2 2 0 2 0 2 2 2 0 0 2 0 2 0 0 0 0 2 2 2 2 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 0 2 2 0 2 0 2 2 0 2 0 2 2 0 0 0 0 0 2 2 0 2 0 0 2 0 2 2 0 0 0 2 2 generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+251x^64+4x^80 The gray image is a code over GF(2) with n=512, k=8 and d=256. This code was found by Heurico 1.16 in 0.234 seconds.