The generator matrix 1 0 1 1 1 X^3+X^2+X 1 1 X 1 1 X^3+X^2 1 1 X^3 1 1 X^2+X 1 1 X^2 1 1 X^3+X 1 1 1 0 1 X^3+X^2+X 1 1 X 1 1 X^3+X^2 1 1 1 1 1 1 1 1 0 X^3+X^2+X X^3+X^2 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 X+1 X^3+X^2+X X^2+1 1 X X^2+X+1 1 X^3+X^2 X^3+1 1 X^3 X+1 1 X^2+X X^3+X^2+1 1 X^3+X X^3+X^2+X+1 1 X^2 1 1 0 X^3+X^2+X X+1 1 1 1 X^3+X^2 X^3+X^2+X+1 1 X X^3+X^2+1 1 0 X^3+X^2+X X^3+X^2 X X^3+X+1 X^3+X^2+1 X^3+X^2+X+1 1 1 1 1 1 X^3 X^2+X X^3 X^2+X X^3 X^2+X 0 X^3+X^2+X X^2 X^3+X X^2 X^3+X X^3+X^2 X X^2 X^3+X X^3+X+1 X^2+1 X^2+X+1 X^3+X^2+X X^2+1 0 0 X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 0 X^3 X^2 0 X^2 0 X^2 0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^3 X^2 X^3+X^2 0 0 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 0 X^2 X^3 X^3+X^2 X^3 X^2 0 X^3 X^3+X^2 0 X^2 X^3+X^2 X^3 X^2 0 X^3 X^3+X^2 X^2 0 X^3+X^2 X^3 0 X^2 X^3 X^3+X^2 X^2 X^2 0 generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 67. Homogenous weight enumerator: w(x)=1x^0+240x^67+68x^68+432x^69+48x^70+208x^71+9x^72+16x^73+1x^96+1x^104 The gray image is a linear code over GF(2) with n=552, k=10 and d=268. This code was found by Heurico 1.16 in 2.25 seconds.