The generator matrix 1 0 0 0 1 1 1 2 2X+2 2 2X+2 1 1 1 1 1 X 1 1 1 1 X+2 1 X 2X 2 1 1 1 1 1 X 2X+2 3X 1 3X+2 1 3X+2 3X 1 X+2 0 3X+2 1 0 2X X 1 1 1 1 1 1 X+2 1 2 1 1 2X 3X+2 2 3X 3X 3X+2 1 X+2 2X 2X 1 3X+2 1 0 1 0 0 2X 1 2X+1 1 1 1 X 3X+1 0 3X+2 X+1 2X+2 X+2 2X+3 X+3 2X+2 2 2 2 2X 1 1 X 1 3X+3 3 3X 1 1 3X 3 1 2X 2 1 3X+1 1 2X+2 3X X+2 1 1 1 X X+3 2X+3 2X+1 3 3X+1 X 3 1 X+2 3X+3 X+2 1 0 2 1 X+2 X+3 2 0 1 2X+3 2X 0 0 0 1 0 2X+1 1 2X 2X+1 0 3 1 3X+3 X+3 X+2 2X+2 2 1 3X+3 3 3X 2X+1 X X+1 1 X+3 3X 2X+1 2X+2 X+3 2X+2 0 2 X+1 1 X+2 2X+2 X 1 3X+2 2X+3 0 1 X+2 3X+3 X+3 X+2 1 2X+3 3X 2X+2 2X+3 X+2 2X 0 X 2X 3X+2 X+2 1 X+3 1 1 2 1 3X+3 0 2X+2 3X+3 1 1 0 0 0 0 1 1 2X 2X+1 2X+1 3 2X+2 3X+3 3X+3 2X+2 X+1 3X 3X+1 X 3X 1 0 X+3 1 X 3 X+3 3X+1 3 3X+3 2X+1 3X X+3 2 2X+2 3X+1 3 2X+1 2X+3 3X 2X+2 2X X+1 2X+3 1 2X+3 3 3X+2 3X+2 2 X+1 2 X 3X+1 3X+1 1 X+2 3X X 2X+2 2X+3 1 X X 2X 3X+2 X+2 1 1 2X X+2 X+3 2X generates a code of length 71 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+224x^64+1334x^65+2439x^66+4482x^67+5244x^68+7690x^69+7451x^70+8374x^71+7482x^72+7558x^73+5140x^74+4160x^75+1849x^76+1216x^77+483x^78+182x^79+103x^80+56x^81+37x^82+18x^83+9x^84+2x^85+2x^90 The gray image is a code over GF(2) with n=568, k=16 and d=256. This code was found by Heurico 1.16 in 37 seconds.