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 X^2 1 1 1 1 1 1 1 0 1 1 1 1 X X 1 1 1 1 X X 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X X^2 0 X^2+X X 0 X^2 X^2+X X X^2 0 X^2+X X^2 X^2+X X X^2 X 0 X^2 X^2+X X^2 X^2+X X 0 X 0 0 X^2+X X^2+X 0 X^2 X^2+X X^2+X 0 X^2 X 0 X 0 X^2 0 X^2+X X^2+X X X 0 X^2 X^2 0 X^2 X^2+X X^2+X 0 X^2 0 X X^2 X^2 X^2+X X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 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 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 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 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+58x^68+78x^70+155x^72+128x^73+304x^74+128x^75+58x^76+32x^78+19x^80+24x^82+20x^84+10x^86+8x^88+1x^136 The gray image is a linear code over GF(2) with n=296, k=10 and d=136. This code was found by Heurico 1.16 in 0.357 seconds.