The generator matrix 1 0 0 0 1 1 1 1 X+2 X^2+X+2 1 1 1 2 X 1 1 1 0 1 X^2 1 X^2+X+2 X^2+X X 1 1 X 1 1 X^2+X 1 X^2+X X^2+X+2 1 1 X^2+X+2 1 1 X+2 X+2 X+2 1 X^2+X X^2+X+2 1 1 1 1 2 X+2 1 1 X^2+X+2 X^2+2 1 1 1 X^2+2 1 1 X^2+X+2 1 1 1 0 1 1 X^2+X X 1 X X^2+2 0 X^2 1 X^2 1 X 0 0 X 0 2 1 0 1 0 0 0 X^2+3 2 X^2+X+3 1 X^2 X+3 X^2+3 X^2+2 1 1 0 X^2+X+1 1 X X+3 1 3 X^2+X+2 1 1 X^2 X^2+X+2 X X+2 1 1 X^2+2 1 1 X^2+X+1 X^2+X+2 1 X^2+X+3 2 X^2+X X 1 X^2+X+1 X^2+2 1 X X^2 X^2+X+3 X^2+1 1 1 1 3 1 1 X+2 0 X+2 1 X^2+X+1 X^2+3 1 X^2 X^2+3 X^2+X+3 1 X^2+X 1 2 1 3 1 X^2+X+2 1 1 3 X+2 3 X X^2 X^2 X^2 1 1 2 0 0 1 0 X^2 X^2+2 X^2+3 1 X+1 1 X^2+1 2 X^2+1 X^2+X+1 X^2+X 0 X^2 X 1 3 1 X^2+X+3 0 1 X+2 X^2+X 3 1 X^2+X+1 X+1 X^2+X+2 X+3 X^2 1 X X^2 X+3 X^2+X 3 1 X^2+X+2 3 2 1 0 X^2+3 X+2 X+1 1 X^2+X+2 X^2+3 X^2+2 X^2+X+1 X+2 X X^2+X X^2+X+1 X^2 X+2 X^2 X^2+1 X+1 0 X^2+X 3 X^2+1 X^2+X+2 X^2+X X X^2+X+1 1 X+2 X^2+X+2 X^2+X+2 1 X^2 1 1 X^2 1 1 1 X^2+X+2 1 2 0 0 0 1 X^2+X+1 X+3 X+1 X^2+X+3 X^2+X X+1 X^2+X 2 X^2 1 X^2+1 X+2 1 X^2+X+2 1 2 X^2+X+2 X^2+1 1 X^2+3 X^2+X+1 X^2+X+1 X^2+X 0 3 X^2 2 3 X^2+X+1 X^2+2 X^2+X+3 X^2+X+3 X+1 X^2+X X X^2+1 1 X^2+X X+1 2 X^2 3 X^2+1 X+3 X^2 X+2 X+1 X^2+X+2 X^2+2 X X+1 X^2+2 X+3 0 X^2+1 X^2+X+2 X^2+3 X^2+X X^2+X+3 X^2 3 0 X^2+X+2 X^2+X+1 1 1 X^2+X+2 X^2+X+3 1 X^2+2 X^2+1 X+3 X^2 0 1 2 1 X^2+3 X^2+1 X+2 2 0 0 0 0 2 2 2 2 0 0 2 2 2 0 0 2 2 2 0 2 0 2 0 0 0 2 2 0 2 2 0 2 0 0 2 2 0 0 0 2 2 2 0 2 2 0 0 0 0 2 2 0 0 2 2 0 0 0 2 0 0 2 0 2 0 2 2 0 0 2 0 2 2 0 2 0 0 2 2 2 0 0 0 2 2 generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+446x^77+1848x^78+3504x^79+5413x^80+8078x^81+11112x^82+13084x^83+14036x^84+15982x^85+15053x^86+13332x^87+10532x^88+7720x^89+4822x^90+3046x^91+1737x^92+696x^93+353x^94+130x^95+86x^96+22x^97+28x^98+6x^99+1x^100+2x^103+2x^104 The gray image is a code over GF(2) with n=680, k=17 and d=308. This code was found by Heurico 1.16 in 195 seconds.