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 X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 0 X^2 0 X^3 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 generates a code of length 86 over Z2[X]/(X^4) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+27x^82+36x^83+63x^84+24x^85+726x^86+48x^87+53x^88+8x^89+13x^90+12x^91+9x^92+1x^94+2x^96+1x^166 The gray image is a linear code over GF(2) with n=688, k=10 and d=328. This code was found by Heurico 1.16 in 0.781 seconds.