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 X^2 X X^2 X 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^2 X^3 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 0 X^3 X^3 X^3 X^2 X^3 X^2 X^3+X^2 0 X^2 0 0 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 X^3 X^2 0 X^3+X^2 0 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^2 X^3 0 X^2 X^2 X^3 X^3 0 X^3 X^2 X^3 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 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 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 0 X^3 0 0 X^3 X^3 generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+82x^86+16x^87+210x^88+112x^89+224x^90+112x^91+154x^92+16x^93+66x^94+16x^96+12x^98+2x^108+1x^128 The gray image is a linear code over GF(2) with n=720, k=10 and d=344. This code was found by Heurico 1.16 in 0.875 seconds.