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 X 1 X 1 X 1 1 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 X X X X X X X^2 X X X X X X 0 0 X X^2 X 0 X^3+X^2 0 X^2 0 0 X^2 X^3+X^2 0 0 X^2 X^3+X^2 0 0 X^2 X^3+X^2 0 0 X^2 X^3+X^2 0 0 X^2 X^3+X^2 0 X^2 0 X^3+X^2 X^3 0 X^3 0 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 0 0 X^3 X^3 X^3 0 X^3 X^2 X^2 0 0 X^3+X^2 X^2 0 X^3+X^2 X^2 0 0 X^3+X^2 X^2 0 0 X^3+X^2 X^2 0 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3 X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 0 X^2 X^2 0 X^3 X^2 X^2 0 0 X^3+X^2 X^2 0 0 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^2 0 X^2 X^3+X^2 0 0 X^2 X^3+X^2 X^2 0 X^3 X^3+X^2 X^2 X^3 0 X^2 X^2 X^3+X^2 X^2 X^3+X^2 0 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 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 X^3 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 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 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 X^3 0 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 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+66x^82+16x^83+218x^84+112x^85+242x^86+112x^87+164x^88+16x^89+38x^90+28x^92+6x^94+2x^96+2x^100+1x^128 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 0.734 seconds.