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 X^2 X X^2 X X X 0 1 X X 1 0 1 X^2 1 1 X^2 1 X 1 X^2 1 0 1 1 1 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2 X^2 0 X X^2 X^2+X X 0 X^2 X^2 X 0 X X^2+X X^2 X^2+X 0 X X^2+X X^2+X X^2 X^2 X X^2 X X X^2+X X^2 X^2+X X X 0 X^2+X X X^2 X^2 X^2 0 X^2+X X X X^2+X X^2+X X X^2 X X X X 0 0 X 0 0 0 X X^2+X X X^2 X X^2+X 0 0 X X^2+X X^2+X X^2+X 0 X^2 X X^2+X X^2+X X^2+X X X^2 X^2+X X X^2+X 0 0 X^2 X X^2+X 0 X^2 X^2+X X X^2 0 X^2 X 0 0 X X^2 X^2+X 0 0 X^2+X X X X^2+X 0 X^2 X^2 X^2 X^2+X 0 X X^2 X X 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 X X^2+X 0 0 X^2+X X X^2 X X^2 0 X^2 0 X X 0 X 0 0 X^2 X^2+X X^2 X^2+X X^2+X 0 0 X^2 0 X^2 0 X^2 X X X X^2 X X 0 X^2 X 0 X 0 X^2 X X^2+X 0 X^2 X X^2 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X^2+X 0 X X^2+X X^2 X^2 0 X^2+X 0 X 0 X X^2+X 0 X^2 X^2+X X^2 X^2 X X^2+X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X^2 X^2 0 X X^2+X X^2+X X^2 X 0 0 0 X X^2 X^2+X X^2+X X^2+X X X X^2 X X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 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+52x^53+109x^54+160x^55+266x^56+292x^57+370x^58+458x^59+591x^60+738x^61+720x^62+750x^63+765x^64+752x^65+620x^66+404x^67+309x^68+264x^69+170x^70+120x^71+81x^72+64x^73+53x^74+26x^75+32x^76+10x^77+4x^78+2x^79+3x^80+4x^81+1x^82+1x^94 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 5.57 seconds.