The generator matrix 1 0 0 0 1 1 1 1 1 1 1 X X X^2 X^2+X 1 X^2 1 X^2 1 1 X 1 0 0 1 0 1 X^2 X^2+X 1 X^2 1 X^2+X 1 1 1 1 1 X^2 X X 1 0 X^2 1 X^2+X 1 1 1 0 1 1 1 X 0 X^2+X 0 1 1 X^2+X 0 1 0 0 1 0 0 X 1 X^2+X+1 X^2 X^2+X X+1 X^2+1 1 1 1 X X^2 1 X 1 X+1 X^2 X^2+X X^2+1 1 X^2+X 0 1 0 1 0 1 X X^2+X+1 X 0 1 X+1 X^2 X^2+1 1 X^2+X 1 X^2+X 0 1 0 X^2+X 1 X+1 1 X X^2+X 1 X^2+X 1 0 X^2+X 1 X X 1 1 X^2+X 1 0 0 1 0 0 0 0 1 X^2+1 1 1 X+1 1 X 1 X^2 X X+1 X^2+X+1 X^2+X+1 X+1 1 0 X^2 1 X X+1 1 X^2 1 X^2+1 0 X^2 X X+1 X^2+X X^2+X+1 X^2 X^2+X+1 1 1 X^2+X X^2+X+1 X^2+X X^2+1 1 1 1 X^2+X+1 1 1 X^2+X+1 X X X^2+X 0 1 X+1 X^2 X^2+1 X^2+X+1 X^2+X+1 X^2+X+1 X+1 0 0 0 1 1 X^2+X+1 X^2+X X+1 0 1 X^2+X 1 X^2 X+1 1 X^2+1 X^2 X^2 X X+1 0 X^2+X+1 0 X^2+X+1 X X^2+X X+1 X^2+1 1 X^2+1 X^2 1 1 1 X^2+1 0 X^2 X+1 X X X^2 X^2+1 X^2+X 1 X+1 1 X^2+1 X^2+X 1 X^2+X+1 X^2 1 X 0 X^2 1 X^2+1 X 1 X^2 1 X^2 X X^2+1 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 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 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 55. Homogenous weight enumerator: w(x)=1x^0+286x^55+562x^56+848x^57+1190x^58+1796x^59+1858x^60+2592x^61+2538x^62+3152x^63+3027x^64+3314x^65+2600x^66+2608x^67+2050x^68+1700x^69+975x^70+770x^71+400x^72+228x^73+105x^74+84x^75+36x^76+20x^77+14x^78+8x^79+2x^80+2x^81+1x^86+1x^90 The gray image is a linear code over GF(2) with n=256, k=15 and d=110. This code was found by Heurico 1.16 in 57 seconds.