The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 1 0 1 1 X^2+X X^2+2 1 1 1 1 X+2 1 1 0 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 0 1 X^2+X 1 1 X^2+2 1 1 1 1 X+2 1 1 1 1 1 X 1 1 1 X 1 1 1 1 1 1 1 X 1 1 1 1 0 1 2 X^2+2 X^2+X+2 X 1 2 0 X^2+X 1 1 X 1 X 0 1 X+1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 X+2 1 3 X+1 0 1 X^2+X X^2+1 1 1 X^2+2 X^2+X+3 X+2 3 1 0 X+1 1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 3 1 X+2 X^2+X 1 X+1 1 0 X^2+1 1 X^2+2 X^2+X+3 X+2 3 1 0 X^2+X+2 0 X 2 2 X+2 X X^2 2 X^2+2 X X^2 0 X+2 X+2 0 2 X^2 X+2 X X+1 1 X+3 1 X 1 1 X^2+X 1 X 1 X^2+1 X^2+X+2 X^2+X X^2+3 X^2 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 0 2 2 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 2 0 2 0 2 2 0 0 2 0 2 2 0 0 2 0 2 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 0 2 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 0 0 2 2 0 0 2 2 2 0 0 0 2 2 2 0 0 0 0 0 0 2 2 2 2 0 0 0 2 2 0 2 2 0 0 0 0 2 0 0 2 0 0 0 2 2 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 2 0 2 2 2 0 2 0 0 0 2 2 0 0 2 2 2 2 0 2 0 0 2 0 0 2 2 0 0 2 2 0 2 2 2 2 0 0 0 2 2 2 0 0 0 0 2 2 2 2 0 0 2 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 0 2 0 2 0 0 2 0 0 2 2 2 2 2 0 2 2 2 2 0 2 2 0 0 0 0 0 2 0 0 0 2 0 2 2 0 0 2 2 0 0 0 2 2 0 2 0 0 2 2 0 2 generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+275x^80+232x^81+442x^82+368x^83+597x^84+368x^85+600x^86+360x^87+370x^88+168x^89+194x^90+32x^91+60x^92+12x^94+8x^95+4x^96+2x^100+1x^112+1x^116+1x^128 The gray image is a code over GF(2) with n=680, k=12 and d=320. This code was found by Heurico 1.16 in 0.703 seconds.