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 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 1 1 1 1 1 1 1 1 X^2 1 1 0 X X^2+2 X^2+X 0 X^2+X X^2+2 X+2 0 X^2+X X+2 X^2+2 2 X^2+X+2 X^2 X+2 0 X^2+X X+2 X^2+2 X^2+X 0 X+2 X^2+2 0 X^2+X X^2+2 X+2 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X 2 X^2+X+2 X^2 X 0 X^2+X 2 X^2+X+2 X^2+2 X+2 X^2 X 0 X^2+X 2 X^2+X+2 X^2+X 0 2 X^2+X+2 X^2+2 X^2+2 X^2 X+2 X+2 X X^2 X 0 X^2+X 0 2 2 X^2+X X^2+X+2 X^2+X+2 0 2 X^2+X X^2+X+2 2 X^2+X X^2 X^2+2 X^2 X^2+2 X X X 0 X^2+2 X^2+X+2 X^2+X 0 0 2 0 0 0 2 0 0 0 0 2 0 0 2 0 0 2 2 2 2 0 2 2 0 2 0 2 2 2 2 2 2 0 0 0 0 2 2 2 2 2 2 0 0 0 0 2 2 0 2 0 2 2 2 2 0 0 0 0 0 2 0 2 0 0 0 0 0 0 2 2 2 2 0 2 0 0 2 0 2 0 2 2 0 2 2 2 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 2 0 0 2 0 0 2 0 2 0 2 2 0 0 0 2 2 2 2 2 2 0 2 0 0 0 0 0 2 0 2 0 2 2 0 0 2 2 0 0 2 2 2 2 2 0 2 2 0 2 0 2 0 0 2 0 2 2 0 0 0 0 0 2 0 2 0 0 2 2 2 2 2 0 2 2 0 0 0 2 2 2 0 0 2 0 0 2 2 2 0 0 0 2 2 0 0 2 2 2 2 0 0 0 0 2 2 0 2 0 2 0 2 2 0 0 2 0 0 2 2 2 0 2 0 0 0 2 2 2 0 0 0 2 2 2 0 2 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 0 2 2 0 2 2 0 0 2 0 0 2 2 2 2 2 0 2 2 0 0 0 0 2 0 2 0 2 2 0 0 2 2 0 2 0 2 0 2 2 0 0 2 2 0 0 0 2 2 2 0 2 0 0 2 0 0 2 0 0 0 0 0 2 0 0 2 2 0 0 2 2 0 2 0 0 2 2 2 generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+68x^84+72x^85+82x^86+32x^87+488x^88+560x^89+500x^90+32x^91+72x^92+72x^93+58x^94+10x^96+1x^176 The gray image is a code over GF(2) with n=712, k=11 and d=336. This code was found by Heurico 1.16 in 0.922 seconds.