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+2 X^2+X+2 1 1 X+2 1 X+2 1 1 2 X^2+X+2 1 2 X+2 1 X^2 2 1 1 1 X^2+2 1 0 1 X^2+X 1 X^2+2 2 0 X^2+2 1 X^2+2 X^2 X 1 2 1 X^2+X 1 1 1 1 1 X+2 1 X^2+2 1 1 X^2+X+2 1 X 1 1 1 1 2 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 1 X^2+X+2 X^2 X X^2+X+3 1 X^2 X+2 1 2 X+1 X^2+X+2 1 X^2+2 X^2+X+2 1 X X+1 X+3 1 X^2+1 X^2+2 3 1 0 1 1 1 1 X^2+X 1 1 X+2 X^2+X+2 2 X^2 X^2+2 X^2+X+3 X^2 0 2 X^2+2 X^2+X+2 X^2+X+1 X^2 X^2+X+3 X^2+1 X X^2+3 1 X^2+X+2 3 X^2+X+2 X^2+1 1 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+2 X^2+X X X+3 1 X^2+X+2 X^2+X+3 X X^2+X X+2 1 X^2+X+3 X^2+2 2 X+3 1 1 X^2+3 X^2+2 X+2 X^2+3 3 0 X^2+X+1 X+3 3 X+2 0 X^2 X^2+X+1 X+3 0 X^2+X 1 3 1 X+2 X+2 X^2+X+3 2 X^2+X+3 X^2+X+2 3 1 X+1 1 X^2+1 X^2 1 X^2+X+3 0 X X+2 X^2+3 0 X^2+X+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 X^2+X+1 X^2+2 1 X^2+3 X X^2+2 2 2 X+1 0 3 X^2+3 1 3 X 2 1 X+1 X^2+X+3 X+2 X^2 2 1 X+1 X+1 X X X+3 X^2+X+2 X^2+X+2 3 3 X^2+3 X+2 X^2+2 X+1 X+1 1 2 3 X^2+2 X X+3 X^2+3 X+2 X^2+3 X^2+2 X^2+X+3 X^2+X+1 X^2+X+3 2 X^2+X+2 X^2+1 X^2+1 0 0 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 0 2 2 0 2 0 2 2 2 2 0 2 2 0 2 2 0 0 0 2 0 2 0 2 0 2 2 2 2 0 2 2 2 0 2 0 0 0 0 0 2 0 0 2 2 0 0 0 2 2 0 2 2 0 2 generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+466x^78+1752x^79+3883x^80+5232x^81+8839x^82+9612x^83+13552x^84+14306x^85+16475x^86+14036x^87+13819x^88+9824x^89+8208x^90+4892x^91+3350x^92+1392x^93+797x^94+294x^95+161x^96+72x^97+63x^98+12x^99+16x^100+6x^101+10x^103+2x^104 The gray image is a code over GF(2) with n=688, k=17 and d=312. This code was found by Heurico 1.16 in 197 seconds.