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 1 X X^2 1 1 X^2 1 X X^2+X+2 1 1 1 1 1 1 1 1 1 X+2 1 X^2+2 1 1 1 X^2+X X X 1 X+2 0 2 1 X^2 1 1 X^2 1 1 1 1 1 1 X^2+X+2 X^2+X+2 2 2 1 1 1 1 X^2 2 X X^2+2 1 X^2+2 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 X X^2+X+3 3 1 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^2 1 X^2+3 1 1 X^2 X+1 2 1 X X X^2+2 1 1 3 1 X X^2+X+1 1 X^2+X+2 X^2+X 2 X^2+1 1 X+2 X^2+X 1 X+2 X^2+2 X^2+3 X+3 X+3 2 1 0 X^2 X^2+2 X+1 X^2+X+2 X^2+X X^2+X X^2+X+1 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 1 X+3 X^2+X 2 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 1 X^2+X X^2 1 X^2+X+2 X^2+X+3 1 X+2 1 X^2+X+3 1 X^2+X+2 X^2+X 1 X+3 X^2+3 X^2 X^2+1 X^2+X+3 0 X^2+2 X+3 X^2+X+1 X+1 X 0 1 1 3 X+3 X^2+2 X^2+3 X^2+3 1 X^2+X 0 X+2 1 0 1 2 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 0 3 X^2+3 X^2+2 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+2 X+3 X^2+3 X^2+X X^2+X+3 X^2 X+3 X+1 3 X^2+X X X+2 X X^2+1 1 X^2 2 X^2+2 X^2+3 1 X^2+X+2 3 0 X^2+1 2 1 X^2+X+3 X^2+1 1 2 X^2+2 X^2+X+2 3 X+3 X+3 1 1 X^2+1 2 X^2+2 X+2 X 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 2 0 2 0 0 0 2 2 0 2 2 0 2 0 2 0 0 2 0 0 2 0 2 0 0 0 2 2 2 2 0 0 2 0 2 0 0 2 2 2 0 2 0 2 0 2 2 0 2 0 0 0 0 2 0 2 2 2 2 generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+520x^81+2004x^82+3800x^83+6115x^84+7758x^85+11018x^86+12290x^87+14906x^88+14672x^89+14610x^90+12780x^91+11196x^92+7890x^93+5514x^94+2742x^95+1697x^96+788x^97+424x^98+160x^99+65x^100+76x^101+28x^102+4x^103+4x^104+8x^105+2x^114 The gray image is a code over GF(2) with n=712, k=17 and d=324. This code was found by Heurico 1.16 in 207 seconds.