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 X X 1 1 1 1 0 1 1 1 0 1 X 1 X^2 X X 1 1 1 1 X 1 1 1 X 1 X 1 X 1 1 0 1 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X 0 X^2 X^2 X^2+X X 0 0 X X^2 X^2 X 0 X^2+X X^2+X 0 X^2 X^2 X X^2+X 0 0 0 X X X^2 X^2 X 0 X X X^2+X X X^2 X^2+X X^2 X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X X^2+X X^2 X^2 X 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X^2+X X X X^2 0 X^2 0 X^2+X X^2 X^2 X^2+X X X X^2+X X^2+X X X X 0 0 X 0 X^2+X X^2 X X^2+X X X X^2+X X X X^2 X^2+X X^2 0 X^2+X 0 X X X^2+X X^2 X^2 X X^2+X X^2 X X X^2+X 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 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 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 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 X^2 generates a code of length 63 over Z2[X]/(X^3) who�s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+80x^54+210x^56+56x^57+268x^58+176x^59+259x^60+456x^61+256x^62+672x^63+255x^64+456x^65+218x^66+176x^67+190x^68+56x^69+157x^70+90x^72+32x^74+13x^76+10x^78+4x^80+2x^82+1x^84+1x^86+1x^100 The gray image is a linear code over GF(2) with n=252, k=12 and d=108. This code was found by Heurico 1.16 in 1.35 seconds.