The generator matrix 1 0 0 0 1 1 1 X 1 1 X X 1 1 0 1 1 1 1 2 1 X^2+X X^2+2 X^2 0 1 X^2+X+2 1 1 X^2+X 1 1 X+2 1 X X^2+X 1 X^2 X^2+X 1 X^2+2 1 1 1 1 1 1 2 1 1 0 1 0 X^2 X^2+2 X^2+X+2 X^2 X^2 1 1 1 1 1 X^2+X 1 X^2+2 1 2 1 1 1 1 1 2 1 1 X X 1 1 0 1 0 0 0 X^2+3 X+3 1 1 X+1 X^2+2 1 2 X^2+X+2 1 X+3 X^2+X+1 X^2+2 0 1 X 1 X+2 1 1 X^2+2 X^2+2 X^2+1 X^2+X+1 X+2 X^2+3 X^2+1 1 X^2+X+3 1 1 X 2 1 X^2 X^2+X+2 X^2+X+2 X+3 X X^2+1 X+1 X^2+2 X^2 X^2+1 X^2+X+1 1 X^2+X X^2+X+2 1 X 1 1 X^2 X^2+X+2 X^2 3 X X^2+1 2 X^2+X+1 1 X^2+X+3 X+2 X^2+1 X^2+X+3 X^2+X X^2+X+3 X^2+X+1 1 X^2+3 2 1 2 0 X^2+2 0 0 1 0 X^2 2 X^2+2 0 1 X^2+X+3 1 3 X^2+X+1 X^2+3 3 2 3 X+1 X 2 X^2+X+3 X X+2 X+1 X+1 X^2+2 1 X+1 X+2 1 X X^2+X+1 0 X^2+X X^2 X^2+X+3 X^2+X+3 1 X^2+1 X^2+X X^2+X+2 X+2 1 X+1 X^2+1 X+2 1 1 X^2+X X^2+2 X X+1 1 X^2+1 1 0 1 1 X^2+2 X^2+2 2 X+2 X^2+3 X^2+X X+3 X^2+X+1 2 2 0 X+3 X X^2+3 X^2+X+3 X^2+2 X X^2+X X^2+X+3 1 X^2+X+1 2 0 0 0 1 X^2+X+1 X^2+X+3 2 1 2 X+3 X^2+1 3 X^2 1 X^2+X+2 X^2+3 X+2 X^2+1 X^2+X+2 3 X^2 0 1 3 X+2 X^2+1 X 3 X^2+X+2 X+3 X^2+3 X^2+X X+2 0 X^2+X+1 X^2+2 X^2+X+2 X^2+X X+3 X^2 1 X+3 X+2 X+3 X+1 1 3 X^2+1 X^2+X+2 X+2 X^2+X+3 X^2+2 X^2+X+3 0 X^2+X+2 0 X+3 X^2+X+1 X^2+X+2 X+2 X+2 X^2+1 X^2+1 1 X X 2 1 X^2+2 X+3 1 3 X^2+1 X X^2+2 0 0 X^2+2 X^2+X+1 2 0 0 0 0 2 0 2 2 0 2 2 0 2 0 2 0 0 0 0 2 2 0 0 0 2 2 0 2 2 0 2 2 0 2 0 0 0 2 2 2 2 0 2 2 2 0 0 2 0 2 0 0 2 2 2 2 0 2 2 0 2 2 2 0 0 0 0 2 0 0 0 2 0 0 2 0 2 0 2 0 generates a code of length 80 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+286x^72+1572x^73+3193x^74+5686x^75+8043x^76+10610x^77+12483x^78+15660x^79+15550x^80+16200x^81+13361x^82+10774x^83+7452x^84+5072x^85+2645x^86+1450x^87+586x^88+236x^89+101x^90+60x^91+31x^92+6x^93+8x^94+2x^95+1x^96+2x^100+1x^106 The gray image is a code over GF(2) with n=640, k=17 and d=288. This code was found by Heurico 1.16 in 179 seconds.