The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 0 1 1 1 X+2 1 1 1 X 0 1 1 1 1 X+2 1 1 0 1 1 1 2 1 X+2 1 1 1 0 1 1 0 1 X+2 0 X 1 1 1 1 0 2 1 2 2 1 1 1 1 1 1 2 X+2 0 1 1 1 1 1 1 X X+2 X X X 1 0 1 1 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 1 X+2 X+1 0 1 3 2 3 1 1 X+2 X+1 X X+3 1 0 3 1 X+2 3 0 1 X+1 1 X+2 0 3 1 X+1 0 1 X+2 1 1 1 3 X+3 0 3 1 1 2 1 1 X+1 X+2 1 2 0 X+1 1 1 1 3 X+2 2 X+1 X+1 X 1 1 X 0 X 1 1 X+1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 2 2 2 2 0 0 2 0 2 2 2 0 0 2 0 2 2 0 0 2 0 0 0 2 0 2 2 2 0 2 2 0 0 0 2 2 0 2 0 0 0 2 0 0 0 0 2 2 2 0 0 2 2 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 2 2 2 2 2 0 0 0 2 2 0 2 2 2 2 2 0 0 2 2 0 2 0 2 2 2 0 2 0 2 0 2 2 0 2 0 0 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 2 0 0 2 2 0 2 2 0 0 2 0 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 0 2 0 0 0 2 0 0 2 2 0 0 2 2 0 2 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 0 2 0 0 0 2 2 0 2 2 0 0 0 2 0 2 0 0 2 0 2 0 0 2 0 0 2 0 0 2 2 2 2 2 0 0 2 2 0 0 0 2 2 2 0 2 0 0 2 0 2 0 2 2 0 2 0 2 2 0 0 2 2 0 0 0 0 0 0 0 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 0 0 2 2 2 0 0 0 2 2 0 2 2 2 2 2 0 2 2 0 2 2 0 0 2 0 0 2 0 2 0 2 2 2 2 2 0 2 0 0 2 0 0 0 0 2 2 0 2 2 0 0 0 0 2 0 2 2 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 0 2 0 2 2 2 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 2 2 0 0 2 2 0 2 2 0 0 0 0 2 2 2 0 2 0 0 2 0 2 2 2 0 2 0 2 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 0 2 2 0 0 2 2 2 0 2 2 2 0 2 0 2 2 0 2 2 2 2 0 0 0 2 0 0 2 0 2 2 0 0 2 2 0 2 0 0 0 0 0 0 0 2 2 2 0 2 2 0 2 2 0 2 0 0 0 0 2 0 2 0 0 2 0 generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+99x^70+40x^71+260x^72+132x^73+425x^74+292x^75+636x^76+496x^77+783x^78+576x^79+835x^80+568x^81+759x^82+504x^83+564x^84+304x^85+398x^86+120x^87+215x^88+36x^89+65x^90+4x^91+28x^92+12x^94+12x^96+13x^98+4x^100+3x^102+5x^104+2x^106+1x^110 The gray image is a code over GF(2) with n=320, k=13 and d=140. This code was found by Heurico 1.16 in 20.9 seconds.