The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 2 1 2 1 1 1 X 1 X 1 1 1 X+2 1 1 1 X 1 1 0 1 X 1 1 1 1 0 0 X 1 1 2 1 0 1 0 1 1 X X 1 1 1 X+2 1 1 1 X+2 X+2 0 X X 1 1 1 1 1 1 1 1 X 1 1 1 1 0 1 1 X+2 X+3 1 0 X+1 1 X 1 3 0 1 1 1 2 3 X+2 1 X+3 1 X X+1 0 1 X+3 2 1 1 X+2 3 1 X+2 1 3 3 X+3 X+2 1 1 1 2 X 1 X+1 1 2 1 0 X+1 1 1 2 X+3 1 1 X+2 X+1 2 1 1 X 1 X X X+1 3 X X+3 0 1 X+3 1 X+2 X+2 1 0 0 0 X 0 X+2 0 X+2 0 X+2 X+2 X 2 2 X X 0 X+2 2 0 X X 2 X 0 0 2 0 X+2 X+2 X+2 X 0 2 2 0 2 X X 0 2 2 X+2 X X X+2 0 X+2 X 2 0 X+2 X+2 X+2 0 X 0 X+2 2 0 X X 0 X X X+2 0 X 2 X 2 0 X X+2 X 2 2 X 0 0 0 0 2 0 0 0 0 0 0 2 2 0 2 2 2 2 0 0 2 0 0 0 0 2 2 0 0 0 0 2 0 2 2 0 0 2 2 2 2 2 2 2 0 0 2 2 2 0 2 2 2 2 2 2 2 0 0 0 2 2 2 0 2 2 0 0 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 2 0 2 2 0 2 0 2 2 0 2 0 0 2 0 2 0 0 2 2 2 2 2 2 0 2 0 0 2 2 2 0 0 2 2 2 2 0 0 2 2 2 2 2 2 2 0 0 2 2 0 2 0 0 2 2 0 0 2 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 2 2 2 2 0 2 2 2 2 2 2 2 0 2 2 0 0 0 0 0 0 2 2 0 2 2 2 0 2 2 0 2 0 2 0 2 0 2 0 0 0 2 2 2 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 2 0 2 0 0 2 2 2 0 2 2 2 0 2 2 0 0 2 2 0 0 0 2 0 2 2 2 0 0 2 0 0 2 0 0 2 2 2 2 2 0 2 0 2 2 2 2 2 0 2 2 2 0 0 0 0 0 0 0 0 2 2 0 0 2 0 2 0 0 0 0 0 2 2 2 2 0 0 0 2 0 2 0 2 2 2 0 0 2 2 0 0 2 0 2 0 2 2 2 2 2 0 0 0 0 0 2 0 0 0 2 2 2 0 0 2 2 0 2 2 0 0 2 2 2 0 0 0 0 2 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+47x^68+70x^69+158x^70+246x^71+345x^72+442x^73+545x^74+622x^75+661x^76+686x^77+688x^78+712x^79+650x^80+622x^81+481x^82+380x^83+286x^84+186x^85+121x^86+78x^87+41x^88+38x^89+31x^90+6x^91+13x^92+2x^93+14x^94+4x^95+3x^96+2x^97+7x^98+1x^100+3x^102 The gray image is a code over GF(2) with n=312, k=13 and d=136. This code was found by Heurico 1.16 in 5.27 seconds.