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 X X X X X X X 1 X X X 1 X 1 2 2 X 1 1 1 1 2 0 2 1 1 X 1 1 2 1 1 X 1 0 X 0 0 0 X X+2 X 0 2 2 X X+2 X X 0 0 0 2 X+2 X+2 2 X+2 X X+2 0 0 X+2 X 0 X 2 X 0 X X 0 X+2 2 X+2 X X+2 X+2 X+2 2 X X 0 X X+2 0 X 2 0 X X X 2 X+2 X X+2 0 2 0 2 0 0 0 0 X 0 X X X+2 0 0 0 X X X 0 2 X+2 X 0 2 2 0 0 X+2 2 X X+2 2 X+2 0 X+2 X X+2 X X X+2 0 0 2 X 0 X+2 X+2 2 2 0 0 2 X X+2 X+2 X 2 0 0 X+2 X+2 2 X X+2 X+2 X+2 0 X X+2 2 0 0 0 0 0 X X 0 X+2 X 2 X 2 0 X 2 X+2 X 2 2 X X+2 2 X 0 X X+2 X+2 0 X+2 0 0 0 X+2 X+2 X+2 0 X+2 X+2 0 0 0 X+2 X+2 X+2 X+2 X+2 X+2 X 0 2 2 2 X 2 2 X+2 0 0 X+2 2 2 X+2 2 X+2 X X 2 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 0 2 2 0 2 2 0 2 2 0 0 0 0 2 2 2 2 2 0 0 0 0 2 0 0 0 2 0 0 0 2 2 0 2 0 0 0 0 2 2 2 2 2 0 2 2 0 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 2 2 0 0 0 2 0 0 0 0 2 2 0 0 2 2 0 2 0 2 2 0 0 2 2 2 0 2 0 2 2 2 0 0 2 0 2 2 2 2 0 2 0 2 0 0 2 0 0 0 0 0 0 0 0 2 0 2 0 0 2 2 2 0 0 2 0 2 2 2 0 2 0 0 0 2 0 0 0 2 2 0 2 2 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 0 0 2 0 0 2 0 0 0 0 2 0 2 2 2 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 2 2 0 0 2 2 0 0 0 2 2 0 2 0 2 0 2 2 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 2 2 2 0 2 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+40x^56+62x^57+129x^58+172x^59+259x^60+314x^61+394x^62+484x^63+552x^64+616x^65+749x^66+826x^67+717x^68+690x^69+498x^70+378x^71+296x^72+300x^73+195x^74+146x^75+155x^76+60x^77+65x^78+42x^79+23x^80+6x^81+13x^82+5x^84+2x^86+2x^90+1x^94 The gray image is a code over GF(2) with n=268, k=13 and d=112. This code was found by Heurico 1.16 in 5.72 seconds.