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 X 0 1 1 X 2X+2 1 1 1 1 1 1 X 0 X 2X+2 X X X X X X 2X 2 X X 2X 2 1 1 X X X X 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 2 1 2 2 2 0 X 2X+2 X+2 0 X+2 2X+2 3X 2X 3X+2 2 3X 2X 3X+2 2 X 0 X+2 2X+2 3X 0 X+2 2X+2 3X X+2 X 2X 3X+2 3X X 2 X 2X 3X+2 2 X X+2 X 3X X 0 2X+2 3X+2 X 2X 2 X X 3X+2 X X X 0 2X+2 0 2X+2 2 2X 0 2X+2 2X 2 X+2 3X X+2 X 2X+2 0 3X+2 2X 3X 3X+2 X 2X+2 2X 2 2X 2 0 0 2X 2X 2X 0 0 2X 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 2X 0 0 generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+56x^77+143x^78+32x^79+15x^80+8x^85+1x^94 The gray image is a code over GF(2) with n=624, k=8 and d=308. This code was found by Heurico 1.16 in 2.47 seconds.