The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 1 0 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 X^2+X 1 1 0 1 1 1 X^3+X^2 1 X^3+X 1 1 X^2 X 1 1 1 1 1 X^3+X^2 1 X^3+X 1 X 1 1 1 0 0 1 X^3 X^3+X 1 1 1 X 1 1 1 X^2+X X 1 X^2+X X^3+X^2+X X^3 1 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 0 X+1 1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 X^3+X 1 0 X^3+1 1 X^3+X^2+X+1 X^3+X^2 X+1 1 X^2+1 1 X^2+X X^3+X+1 1 1 X^2+1 0 X^2+X X^3 X+1 1 X^3+X 1 X^2+1 X^3+X^2 X^3+X^2+1 X^3+1 X^3+X^2+X 1 1 0 X 1 X^3 X+1 X^3 1 X^3+X+1 X^2+1 X^3+X 1 1 X^3+X^2 1 1 1 X^2+1 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 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 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+22x^66+98x^67+442x^68+316x^69+469x^70+318x^71+813x^72+280x^73+540x^74+270x^75+333x^76+108x^77+54x^78+18x^79+8x^80+1x^82+1x^88+1x^90+1x^92+1x^94+1x^96 The gray image is a linear code over GF(2) with n=576, k=12 and d=264. This code was found by Heurico 1.16 in 0.469 seconds.