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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 0 X 0 X 2 X 0 0 0 0 X 1 X 1 X 1 1 1 1 X 2 1 1 1 X 0 X 0 0 0 0 0 0 0 X X+2 X X X+2 2 0 X 2 X+2 X X 2 X X X 0 0 2 0 0 2 X+2 0 X+2 X 2 X+2 X+2 0 2 X X+2 X 0 0 X+2 2 X 0 X X 0 2 X 2 2 2 0 0 X+2 0 2 X X+2 X 2 2 0 0 X 0 0 0 X X+2 X 0 0 0 X X 0 X 2 X X+2 X+2 0 2 0 2 X+2 2 2 X X+2 0 X X+2 X 2 X 0 X 2 2 0 0 0 2 X+2 0 X 2 X 2 X+2 2 0 X X+2 X+2 X+2 X+2 2 X+2 X 2 0 X+2 X+2 X 2 0 0 0 0 X 0 X X X+2 0 X X 2 0 2 X+2 X X 0 X+2 X+2 2 X 0 0 2 X 0 X 0 X+2 X+2 X 2 0 2 X X 0 2 X 0 X+2 2 X X 2 X X+2 0 2 0 X 2 0 X+2 X+2 X+2 0 0 X X 0 0 X+2 X+2 X+2 0 0 0 0 0 X X 0 X+2 X 2 X+2 X+2 0 X+2 2 2 X 0 0 X 2 0 X+2 2 X X X X 0 0 0 X+2 X 0 0 X 2 X 0 0 2 X+2 0 X 2 X+2 X+2 X+2 X X 2 2 0 X 0 X+2 X+2 0 X X 0 X+2 X+2 X X X X 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 2 0 2 2 0 0 0 0 0 2 0 2 0 2 0 2 2 2 2 2 0 0 2 0 0 2 0 2 2 2 0 0 0 0 0 0 2 2 2 0 2 2 2 0 0 0 0 2 2 2 0 0 0 0 0 0 2 0 2 2 0 2 0 0 2 0 2 2 0 2 0 2 0 2 2 0 2 2 2 2 2 0 0 2 2 0 2 0 0 0 0 2 0 0 2 2 2 2 2 0 0 0 2 2 0 2 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 2 2 2 0 2 0 0 2 0 2 0 2 2 2 0 0 2 0 0 2 2 0 2 0 0 2 0 2 2 2 0 2 2 2 0 0 0 2 0 2 0 2 0 0 0 0 2 2 2 0 2 0 0 0 generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+207x^56+458x^58+48x^59+744x^60+308x^61+816x^62+844x^63+950x^64+1840x^65+960x^66+2056x^67+1052x^68+1928x^69+872x^70+848x^71+802x^72+272x^73+530x^74+40x^75+486x^76+4x^77+184x^78+4x^79+103x^80+20x^82+5x^84+1x^88+1x^100 The gray image is a code over GF(2) with n=268, k=14 and d=112. This code was found by Heurico 1.16 in 21.5 seconds.