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 X X 0 0 1 1 1 0 X X 0 1 X 1 X^2 1 X 1 X X 1 0 1 X X 1 X X^2 0 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 0 X X^2 X X^2+X X 0 X^2 X X X^2 0 X 0 0 X^2+X X^2 X^2+X X^2+X X X^2 0 X^2+X X^2 X^2+X X^2+X X^2 X^2+X 0 X^2 0 X^2 X^2+X X^2+X X^2 X^2+X X^2 X 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 X^2+X X^2+X X^2 X^2 X^2 X X^2+X X X^2 X^2+X X X X X^2 X^2+X X^2 0 0 X^2+X 0 X^2 X^2+X 0 X^2 X^2 X^2+X X X^2+X X^2 0 X X X^2 X^2 0 X^2 0 X 0 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 X^2 X^2 X 0 X X^2 0 X^2 X X^2+X X^2+X X^2 0 X^2 X^2 0 X X^2 X^2+X X X^2+X 0 X^2 X X^2+X X^2 X X^2 X^2+X 0 0 X X^2+X X^2+X X^2+X 0 X X 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 X^2 0 X^2 0 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 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 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 0 X^2 X^2 X^2 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 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 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 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 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 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 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 generates a code of length 63 over Z2[X]/(X^3) who´s minimum homogenous weight is 53. Homogenous weight enumerator: w(x)=1x^0+66x^53+146x^54+166x^55+249x^56+296x^57+373x^58+474x^59+592x^60+670x^61+717x^62+826x^63+668x^64+640x^65+650x^66+424x^67+309x^68+286x^69+232x^70+126x^71+88x^72+88x^73+45x^74+30x^75+10x^76+2x^77+9x^78+2x^79+1x^80+4x^82+1x^84+1x^88 The gray image is a linear code over GF(2) with n=252, k=13 and d=106. This code was found by Heurico 1.16 in 21.7 seconds.