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 X 0 1 1 X^2 X 0 X X X 1 X^2 X^2 1 1 1 1 X 0 X 1 0 0 1 X 1 1 X X 1 X 1 X 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2 X^2+X 0 X X 0 X^2 X^2 X^2+X X^2 X X^2+X 0 X X^2 0 X^2 0 0 X^2+X X 0 X^2+X X X^2 X^2 X X^2+X 0 X X^2 0 X X^2 X^2 X X^2+X X 0 X^2 X X X^2+X X 0 X^2 X 0 X X^2+X 0 X^2 X^2+X X 0 0 0 X 0 0 0 X X^2+X X X^2 X X^2+X 0 0 X X X^2 X^2+X X^2+X X^2+X 0 X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2 0 X^2 X^2 X^2+X 0 X^2 X^2 0 X^2 X 0 X^2+X X 0 0 X^2+X X^2+X X X X^2 X^2 X X^2 X X^2 X^2 0 X X X^2 X^2+X X^2+X X^2+X X^2+X X^2 X 0 0 X^2+X 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 X 0 X X X^2+X X^2 0 X^2+X X^2 0 X^2 X^2 X^2 X X^2 X X^2 X^2+X X 0 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X X X^2 X^2 X^2+X 0 X^2+X X^2 X X X 0 0 X^2 X^2+X 0 0 X^2 X X^2+X X 0 X X^2 0 X^2 X^2 X^2 0 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X^2+X X 0 X X^2 X^2 0 X^2 0 X X 0 X X^2 X^2 0 X^2+X X^2 X^2+X X X^2 X^2+X X^2 0 X^2+X X X^2 0 0 X^2+X 0 X^2 X^2 X^2+X 0 X X^2+X 0 0 X^2+X X 0 X^2 0 0 X X X^2+X X^2 X^2+X X^2+X X^2 X^2 X^2+X 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 59. Homogenous weight enumerator: w(x)=1x^0+74x^59+118x^60+198x^61+317x^62+314x^63+365x^64+470x^65+643x^66+652x^67+622x^68+690x^69+771x^70+704x^71+478x^72+494x^73+366x^74+212x^75+206x^76+156x^77+105x^78+76x^79+58x^80+36x^81+30x^82+14x^83+6x^84+4x^85+7x^86+2x^87+2x^88+1x^98 The gray image is a linear code over GF(2) with n=276, k=13 and d=118. This code was found by Heurico 1.16 in 6.43 seconds.