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 1 1 1 1 X 1 1 X^2 X X^2 X X 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 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 0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^2 X^3 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 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 X^3+X^2 X^3+X^2 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 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 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 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 0 X^3 0 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 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 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 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+24x^72+2x^73+42x^74+114x^75+76x^76+492x^77+75x^78+140x^79+27x^80+18x^81+10x^82+2x^83+1x^142 The gray image is a linear code over GF(2) with n=616, k=10 and d=288. This code was found by Heurico 1.16 in 0.5 seconds.