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 1 1 X^2 1 1 X^2 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 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 0 X^3+X^2 X^3 X^3 X^2 X^2 X^3 0 X^3+X^2 X^3+X^2 X^3 X^2 0 X^2 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^3 X^3 X^3 X^2 X^3 0 X^3+X^2 0 0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^2 0 X^3+X^2 X^2 0 X^3+X^2 0 X^2 0 0 X^2 X^2 X^3 X^2 X^3 0 X^2 X^2 X^3 X^3+X^2 0 X^2 0 X^3 X^2 0 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 0 X^3 X^3+X^2 X^3+X^2 X^2 0 0 X^3 X^2 X^3 X^3+X^2 X^2 X^3 X^3 0 X^3 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^2 X^3+X^2 0 0 X^3+X^2 X^3+X^2 X^3 X^2 0 X^3 X^2 X^2 0 X^3 0 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 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 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+161x^68+80x^70+64x^71+567x^72+384x^73+432x^74+64x^75+224x^76+63x^80+7x^84+1x^136 The gray image is a linear code over GF(2) with n=584, k=11 and d=272. This code was found by Heurico 1.16 in 26.9 seconds.