The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X^2 X^2 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 0 2 2 2 2 0 2 2 2 0 2 2 2 0 2 2 0 2 2 2 0 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 2 2 2 0 0 2 2 2 0 2 2 2 0 2 2 2 2 2 2 0 2 2 2 0 2 2 2 0 0 2 0 2 2 0 2 2 0 0 2 0 2 0 2 0 0 2 0 2 0 2 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 2 2 0 0 2 2 0 2 2 0 0 0 0 0 0 2 2 0 0 0 2 0 0 2 2 2 0 0 2 2 0 0 2 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 2 0 2 2 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 2 2 2 0 2 2 2 2 0 2 2 2 0 2 2 2 2 0 2 2 0 2 2 2 0 2 2 2 0 2 0 2 2 0 0 2 2 2 2 0 2 2 2 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 0 2 2 2 0 0 0 0 2 2 2 2 0 0 0 2 2 2 2 0 0 0 2 2 2 2 2 2 0 0 0 2 0 2 0 2 0 2 2 2 0 2 0 0 0 2 0 0 0 0 2 0 2 0 0 2 0 2 2 2 2 0 2 0 0 2 0 0 2 0 0 0 2 2 0 2 2 0 0 2 2 2 0 2 2 0 0 0 0 0 0 2 2 0 2 2 0 2 2 2 0 0 2 0 2 2 2 0 0 2 0 2 2 2 0 0 2 0 2 2 0 0 0 0 0 0 2 2 2 0 2 2 2 2 2 0 0 0 0 0 0 0 2 2 0 2 2 2 2 2 0 0 2 0 0 2 0 2 0 0 0 2 0 2 0 2 2 0 2 0 2 2 2 2 2 2 generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+27x^86+36x^87+33x^88+64x^89+12x^90+700x^91+12x^92+64x^93+13x^94+28x^95+13x^96+4x^98+4x^99+4x^100+7x^102+1x^104+1x^158 The gray image is a code over GF(2) with n=728, k=10 and d=344. This code was found by Heurico 1.16 in 95.9 seconds.