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 X^2 1 1 1 1 1 1 1 1 X^3 1 1 1 1 X^2 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 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 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^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3 X^2 X^3 0 X^2 0 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 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 0 0 X^3 0 0 0 0 0 0 0 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+32x^60+16x^61+55x^62+144x^63+63x^64+784x^65+32x^66+784x^67+8x^68+8x^70+16x^71+16x^72+16x^73+16x^74+16x^75+8x^76+16x^77+16x^78+1x^126 The gray image is a linear code over GF(2) with n=528, k=11 and d=240. This code was found by Heurico 1.16 in 0.375 seconds.