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 X^2 1 1 1 1 1 1 1 1 X^3 1 1 1 1 X 1 1 X X 1 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^2 X^3 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^3+X^2 0 X^3+X^2 0 X^3 X^2 X^3+X^2 0 X^3 X^2 X^3+X^2 X^3+X^2 0 0 X^2 X^3 X^2 X^2 X^3 0 X^3 X^3+X^2 X^3+X^2 X^2 0 X^3 X^3 0 0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 X^3 0 X^3 X^3+X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 0 0 0 0 X^3 0 0 0 0 0 X^3 0 0 0 X^3 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 0 0 0 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 0 0 X^3 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+17x^66+81x^68+125x^70+64x^71+610x^72+384x^73+561x^74+64x^75+31x^76+45x^78+16x^80+10x^82+28x^84+10x^86+1x^136 The gray image is a linear code over GF(2) with n=584, k=11 and d=264. This code was found by Heurico 1.16 in 20.1 seconds.