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 X 0 1 X X 2 1 1 X X 1 1 X 0 X 0 1 1 1 X 1 1 0 2 1 1 1 X 1 1 2 X 1 1 1 1 0 1 1 X 1 1 X X X X 1 1 0 X 0 X 0 0 X X+2 0 2 X 0 X+2 2 X+2 X X+2 0 X 0 X 2 0 X X 0 X+2 X 2 X 0 X+2 2 0 X 2 X X 0 2 X+2 X 2 2 2 2 X+2 X 0 X+2 X+2 X+2 0 X 2 0 2 0 0 X+2 X 2 X X X+2 X+2 0 0 X X X 0 0 0 X X X X+2 X 0 0 0 X X 0 X+2 X 0 0 X X 2 2 X+2 X 2 0 0 X 0 X X X+2 0 X+2 X+2 X 0 X 2 X+2 X X X X X X X+2 0 2 2 X 0 X+2 X X 0 0 X 0 X 2 0 X+2 X X X+2 X 2 2 X+2 0 X+2 0 X+2 X X+2 X X+2 2 0 X+2 X+2 X+2 2 X 2 X+2 X 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 2 2 2 2 2 0 0 0 2 2 0 0 0 2 0 2 0 0 2 2 2 0 0 0 0 2 2 0 2 0 2 2 2 2 0 2 2 0 0 2 2 0 0 0 0 2 0 2 2 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 0 2 2 0 2 2 2 0 0 0 2 0 2 2 0 0 0 2 2 2 2 0 2 0 2 2 2 2 2 0 0 2 0 0 0 0 0 2 0 0 0 2 0 2 2 2 2 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 2 0 2 0 0 2 2 0 0 2 2 2 2 0 2 0 0 0 2 0 2 0 0 2 2 2 2 2 0 2 2 0 2 2 0 2 0 0 2 0 0 2 0 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 0 2 0 2 0 0 2 2 2 0 2 0 2 0 2 0 0 2 2 2 0 0 0 2 2 2 2 2 2 2 0 0 2 0 2 0 0 0 0 2 2 2 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 0 0 2 2 0 2 0 2 2 2 2 2 0 2 0 0 0 0 0 0 0 2 2 2 0 2 0 2 0 0 2 2 0 0 0 0 0 0 0 2 2 0 2 2 2 0 2 2 2 2 0 2 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 0 2 0 2 2 2 2 2 2 2 0 0 0 0 2 2 0 0 0 2 0 0 2 0 0 0 2 0 0 2 2 0 2 0 0 0 0 0 0 0 2 0 generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+41x^68+42x^69+108x^70+146x^71+230x^72+234x^73+290x^74+420x^75+496x^76+564x^77+518x^78+652x^79+732x^80+720x^81+680x^82+516x^83+378x^84+350x^85+284x^86+246x^87+123x^88+118x^89+110x^90+56x^91+36x^92+20x^93+34x^94+12x^95+9x^96+13x^98+1x^100+8x^102+1x^104+2x^106+1x^114 The gray image is a code over GF(2) with n=320, k=13 and d=136. This code was found by Heurico 1.16 in 7.93 seconds.