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 1 X^3 1 1 1 X 1 1 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 0 X^2 X^3+X^2 X^3 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^2 X^3 X^3+X^2 0 0 X^3+X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^2 0 0 X^3+X^2 X^3 X^3+X^2 X^2 0 X^3 X^2 0 0 X^2 X^3 X^2 X^3 0 0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 0 X^3 X^3 X^3+X^2 X^2 X^3 X^3+X^2 X^2 0 X^3 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 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 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 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 0 X^3 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 0 X^3 0 0 0 0 X^3 0 0 X^3 0 0 X^3 0 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 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 0 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+38x^68+52x^70+144x^72+64x^73+584x^74+384x^75+577x^76+64x^77+24x^78+39x^80+24x^82+24x^84+20x^86+8x^88+1x^140 The gray image is a linear code over GF(2) with n=600, k=11 and d=272. This code was found by Heurico 1.16 in 0.563 seconds.