The generator matrix 1 0 0 0 1 1 1 1 2 1 X+2 X^2+X+2 1 X^2+X 1 1 1 0 1 X^2+X+2 1 1 X^2+X+2 1 X^2+X+2 1 1 2 X^2+X X^2 X^2+X+2 1 1 1 0 1 2 X^2+2 1 X^2+2 2 X 1 1 X^2+2 2 1 X^2+2 1 X 1 X^2+2 1 1 X^2 1 1 1 X+2 X^2 1 X^2+2 2 X^2+X X 1 0 1 X^2+X+2 2 1 X 1 X^2+X+2 1 1 1 0 1 0 0 X X^2+1 2 X^2+3 1 X^2+X+2 X 1 3 1 X^2+X+3 X+1 X^2+2 1 0 1 X^2+X+2 X^2+X+1 1 X^2 X^2 1 X+1 X+2 X^2+X 1 1 3 X X X^2+X 1 X^2+X 1 X^2+X+1 1 X^2+X+2 1 X+2 X^2+X X^2 1 X^2+1 0 3 2 X^2+X+2 1 X^2+1 0 1 1 X^2+X 3 1 X^2+X+2 X^2+X+3 2 1 1 1 X^2+3 0 X 1 1 X^2+X+1 0 X^2+2 X^2 X+3 X+1 2 0 0 1 0 0 2 X^2+3 X^2+1 1 X^2+1 1 3 X^2+X+2 X+2 3 X^2+X+2 X+1 X^2+X+1 X X^2+1 X+2 X+3 X^2+2 X^2+X+1 1 X^2+1 X X^2 1 X^2+X+2 X^2+X+1 X^2+X+1 X+1 X^2 1 X+3 1 X^2+3 X^2+X+2 0 X+2 X^2+2 X^2+X+1 X^2 1 X^2+2 X^2+X 1 X+2 X X^2+X X^2+X+1 X^2+2 X^2+3 1 0 1 X+1 X^2 1 3 X^2+X+2 X+1 X^2+3 X+2 X+3 1 X^2+X+1 X^2+X X X+1 1 X+3 1 X^2+X+1 0 0 0 0 0 1 1 X+3 X+1 2 X^2+X+3 X+2 X^2+X+1 X^2+X+2 X^2+X X+3 X+1 X^2+3 2 X 3 3 0 X^2 X+1 X^2+X+1 X^2+X 1 X^2+2 1 3 0 X^2+2 X^2+2 X^2+X+2 X+1 3 1 0 X^2+X+1 X^2+X+3 X+1 1 X^2+X+2 X^2+3 0 X^2 X^2+X+2 X^2+1 X^2+1 X 1 X^2+X X^2+X+2 3 X X^2+X+2 X^2+X+3 X^2+1 X+2 X+1 X^2+2 X^2+1 1 X^2+X+1 X^2+X+3 1 X+3 X 1 X X+1 X^2+X 3 X+1 X+1 3 X^2+X X^2 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 0 2 2 2 0 0 0 2 0 0 2 2 0 2 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 2 2 2 0 2 0 0 2 0 0 0 2 0 0 0 0 0 2 2 0 0 0 2 2 generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+290x^69+1429x^70+2944x^71+5371x^72+7778x^73+10228x^74+13892x^75+15321x^76+16764x^77+15638x^78+13650x^79+10832x^80+7304x^81+4667x^82+2694x^83+1263x^84+602x^85+219x^86+94x^87+40x^88+30x^89+8x^90+6x^91+4x^92+2x^94+1x^98 The gray image is a code over GF(2) with n=616, k=17 and d=276. This code was found by Heurico 1.16 in 169 seconds.