The generator matrix 1 0 0 0 1 1 1 1 X 1 X 1 X^2+X+2 1 X X 1 0 1 1 X^2+X+2 X^2+X X^2+2 1 0 1 1 1 X 1 X 1 X^2 1 1 X^2 1 X X^2+X+2 1 1 1 1 1 1 1 1 1 1 X^2+2 X^2+2 X^2+2 1 2 1 X+2 1 X^2+X+2 0 1 1 X^2+2 1 1 0 1 1 1 2 0 X^2+X 1 1 X^2+2 1 2 1 X^2 1 X X+2 X^2+2 X^2 1 1 1 1 1 0 1 0 0 0 X^2+3 2 X^2+X+3 1 X^2 X^2 X+3 1 3 1 X^2+X X^2+X+2 1 X^2+X X^2+3 1 1 X 1 1 0 1 X^2+X 1 X^2+X+3 X 3 X^2+2 X^2+X X+1 1 X^2+X X^2+X X^2+2 X 2 X+3 3 2 X+1 X+3 X^2+X+3 X+1 X+2 2 1 1 1 1 2 1 X^2+X+3 X^2 1 3 X^2+2 X+2 X^2 X 1 X+3 X^2 X^2+X+2 X 1 1 X+1 X+2 1 X^2+X 1 X 0 X 1 2 X+2 1 X^2+2 X^2 X+3 X+3 3 0 0 1 0 X^2 X^2+2 X^2+3 1 X^2+X+3 X^2+3 1 X^2+X X+2 X+1 X^2+X+1 X^2+X+2 0 X^2 X^2+1 X X+3 X^2+X 1 X^2+3 X^2+1 X+3 X+3 X^2 2 X+3 1 X^2+X X^2+X 0 X+3 X^2+X+1 X^2+X+1 1 1 1 3 X^2+2 X X+2 X^2+3 X^2+1 X^2+2 X^2+X+3 X^2+X+1 1 X^2 X+2 1 X+2 X+2 X^2+1 X^2+X 1 X^2+3 1 X^2+2 1 X+2 X+3 1 X^2+X+3 X^2+X+1 X^2+X+3 2 X^2+X+3 X^2+X+3 X+2 X^2+X 0 X+2 X^2+X+1 X^2+1 X+2 X^2+2 X^2+X 1 X X^2+3 0 3 X^2+X+1 X^2+X+2 X+1 0 0 0 1 X^2+X+1 X+3 X+1 X^2+X+3 X+2 X^2+X+2 X+3 X^2+X X^2+3 2 X^2+3 1 X+1 3 X^2+X+3 X^2+2 X+1 X+2 X^2+X+3 1 X+2 X+2 X^2+X 0 X^2+2 3 0 X^2+3 1 X+2 2 0 X+3 X^2+1 X^2 X^2+3 X^2 X^2+3 X^2+X+2 X^2+1 0 1 X+1 X+3 X^2+1 X^2+3 X^2+X X+3 X^2+X+3 2 X X+1 X^2+X+1 X^2+X X^2+X+1 1 X^2+X X^2+3 X+1 2 X^2+X+2 X+2 X+1 X^2+X+2 1 1 X X^2+1 X X+3 0 X+1 X^2+2 1 X^2+X+3 X^2+2 0 1 X^2+X+3 X^2+X+1 X^2+3 X^2+2 X^2+1 1 0 0 0 0 2 2 2 2 0 0 2 0 2 0 2 2 2 2 2 0 2 0 2 2 0 0 0 0 0 2 0 2 2 0 0 0 2 2 0 2 2 0 2 0 2 0 0 0 0 0 2 0 0 2 2 0 0 2 0 0 2 0 0 2 2 0 2 2 0 0 2 2 2 0 2 2 2 0 0 0 2 2 2 0 0 2 0 2 generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+577x^80+1830x^81+3559x^82+6084x^83+8224x^84+10646x^85+12818x^86+14502x^87+14811x^88+15018x^89+13081x^90+10218x^91+8017x^92+5668x^93+2895x^94+1670x^95+807x^96+326x^97+172x^98+58x^99+35x^100+14x^101+19x^102+12x^103+8x^104+2x^105 The gray image is a code over GF(2) with n=704, k=17 and d=320. This code was found by Heurico 1.16 in 229 seconds.