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 X 1 1 1 1 1 1 X 1 1 1 X 1 1 1 1 1 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+70x^68+87x^72+96x^74+512x^75+136x^76+32x^78+50x^80+34x^84+5x^88+1x^144 The gray image is a linear code over GF(2) with n=300, k=10 and d=136. This code was found by Heurico 1.16 in 0.335 seconds.