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 X 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 1 1 1 X 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^2 0 X^3+X^2 X^3 X^3+X^2 0 X^3+X^2 X^2 X^3 0 X^3+X^2 X^2 0 X^3 X^3+X^2 X^2 0 X^3 X^3+X^2 X^2 0 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^3 X^2 X^2 X^2 0 0 X^3 X^2 X^2 0 0 X^3 X^3 0 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 0 0 X^3 X^3 X^3 0 X^3+X^2 X^3+X^2 0 X^3 X^3+X^2 X^3+X^2 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 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 0 0 X^3 0 0 0 X^3 0 0 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 X^3 0 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 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 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 X^3 0 generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+56x^68+64x^70+170x^72+640x^73+316x^74+640x^75+55x^76+28x^78+13x^80+20x^82+24x^84+20x^86+1x^140 The gray image is a linear code over GF(2) with n=592, k=11 and d=272. This code was found by Heurico 1.16 in 0.594 seconds.