The generator matrix 1 0 0 0 1 1 1 1 2X 1 1 0 1 2 2X+2 1 X+2 1 X 1 3X+2 X+2 2X 1 3X+2 1 1 1 1 3X 2X 0 2X+2 3X 2X 1 3X 1 1 1 1 1 2X 1 2X+2 1 1 1 X+2 1 1 1 1 1 2X+2 0 3X 1 1 1 1 X 1 2X+2 1 3X 1 1 0 1 0 0 X 3 3X+2 3X+3 1 3X 2X+3 1 3 1 2X 2X 2X 2 1 3X+1 1 3X+2 1 2X+1 X X+3 2X+2 3 X+2 1 X 2 1 0 1 2X+1 1 3X X+1 3X+1 3X X+2 1 2 1 2X X 3 1 2X 3X 3X+1 2 X+2 3X 1 1 2X X+2 1 2 2X 3X+1 2X X+1 2 3X 0 0 0 1 0 0 2X 3X+1 2X+3 3 3 X+1 X+2 3X X+1 1 X 3X+2 X+3 X+1 1 X 1 X+3 2X 1 2 3X+3 3 2 3X+2 1 1 3X+3 0 2X+1 3 1 X+3 2 2 3X X+2 3X 2X+2 2X+3 1 3 X+3 2 X+2 1 3X+2 X+3 X+1 3X+2 2X 3X 0 3X 1 2X 1 3X 2 3X+1 X 3X+3 2 0 0 0 1 1 3X+1 X+1 2X+3 X X+2 2 3X+1 3X 2X+1 3 2X 1 X+3 2X+3 0 2 0 3X 3X+2 3X+3 3X+1 3X+2 3X+1 3X+3 1 X+3 X 3X+1 1 X+1 2X+3 2X 3 3 3X+2 3X 1 0 2 2 3X+3 X+2 X X+3 2X+3 2X 2X+2 1 3X 1 2X+2 X X+3 X+1 0 X 3X X+3 1 0 1 2X+2 2 0 0 0 0 2X 2X 2X 2X 0 2X 2X 0 2X 0 0 2X 0 2X 0 2X 0 0 0 2X 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 2X 0 0 0 0 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 0 2X 0 2X 0 0 0 2X 2X 2X 0 0 generates a code of length 68 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+130x^60+998x^61+2599x^62+4438x^63+7601x^64+10014x^65+14477x^66+15878x^67+18533x^68+16140x^69+14965x^70+10658x^71+6983x^72+3766x^73+2263x^74+860x^75+457x^76+178x^77+56x^78+36x^79+23x^80+8x^81+4x^82+2x^83+4x^86 The gray image is a code over GF(2) with n=544, k=17 and d=240. This code was found by Heurico 1.16 in 141 seconds.