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 X^2 X 0 X X^2 0 1 1 X^2 X X^2 0 1 0 1 0 X^2 1 X 1 1 1 1 X 1 X 0 1 1 1 X 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X X X 0 0 0 X^2 X^2+X X^2+X X^2 X^2+X X X^2+X 0 0 X^2+X 0 X X X^2 X X^2 X^2+X X X 0 0 X X X 0 X^2 X^2 X X X^2 0 X^2 X 0 X X^2 0 0 X^2+X X^2 X X^2 X X X^2+X X^2 X^2 0 0 0 X 0 X X X^2+X 0 0 0 X X X 0 X^2 X^2+X X 0 X^2 X^2 0 0 X^2+X X^2 X X^2+X X^2 X^2+X X^2+X 0 X X^2+X X X 0 X 0 X X^2+X X^2 X^2+X X^2 X^2 X X X^2+X 0 0 X X X^2+X X^2 X^2 X^2 X^2 0 X^2+X X^2+X 0 X^2+X X^2 0 X^2+X 0 0 X^2 0 0 0 X X 0 X^2+X X X^2 X X^2 0 X X^2 X^2+X X X^2 X^2 X X^2+X X^2 X 0 X X^2+X X^2+X 0 X^2+X 0 0 0 X^2+X X^2+X X^2 X^2 0 X^2+X 0 0 X^2+X X^2+X X^2 X^2 X^2+X 0 0 X^2 X X^2 0 X^2 X X^2 X^2+X X^2+X X^2+X X^2+X 0 0 X^2+X X X X^2+X X^2 X^2+X X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 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 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 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 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+172x^56+276x^58+24x^59+585x^60+168x^61+604x^62+328x^63+987x^64+472x^65+1036x^66+552x^67+929x^68+344x^69+592x^70+120x^71+463x^72+40x^73+244x^74+147x^76+52x^78+39x^80+12x^82+3x^84+1x^88+1x^96 The gray image is a linear code over GF(2) with n=264, k=13 and d=112. This code was found by Heurico 1.16 in 5.97 seconds.