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 X 0 1 X 0 1 1 X 1 1 0 X 0 1 1 X 0 1 X 1 1 1 1 0 X 1 1 0 1 1 1 1 X 1 1 1 1 X X 1 1 X^2 X^2 1 X 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X X^2 X^2+X 0 X^2+X 0 X^2 X X^2+X X 0 X^2+X X 0 X^2+X X^2+X X^2 X^2+X X X^2+X X X^2+X X X^2+X X X^2+X X^2+X X^2 0 X^2+X X^2+X X X^2+X X^2 X^2 X X^2 X^2 0 X X^2+X 0 X X^2 X X^2+X X X X X^2 X^2 0 X^2+X 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 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 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 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 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+120x^56+52x^58+8x^59+424x^60+48x^61+292x^62+224x^63+889x^64+616x^65+700x^66+1296x^67+1122x^68+1952x^69+968x^70+1856x^71+1253x^72+1232x^73+716x^74+680x^75+755x^76+240x^77+308x^78+32x^79+379x^80+8x^81+36x^82+125x^84+43x^88+5x^92+3x^96+1x^100 The gray image is a linear code over GF(2) with n=280, k=14 and d=112. This code was found by Heurico 1.16 in 25 seconds.