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 X 1 X 1 X 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 X X^2 X X X X 0 X X X^2 X 0 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 0 X^2 X^3+X^2 0 X^3 0 X^3 X^2 X^3 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^2 X^3+X^2 X^3 0 X^3 0 X^3 X^3 X^3 X^2 X^2 X^3 X^2 X^3 X^3 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^2 X^3+X^2 X^3 X^3 X^2 X^2 X^2 X^3+X^2 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^2 X^3 0 X^2 X^3+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 0 X^3 X^2 X^3+X^2 X^3 X^2 0 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^2 0 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 0 X^3 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 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 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 0 X^3 0 X^3 0 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 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 85. Homogenous weight enumerator: w(x)=1x^0+64x^85+76x^86+184x^87+46x^88+292x^89+88x^90+180x^91+8x^92+24x^93+28x^94+16x^95+6x^96+4x^97+4x^99+2x^104+1x^128 The gray image is a linear code over GF(2) with n=712, k=10 and d=340. This code was found by Heurico 1.16 in 0.828 seconds.