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 1 1 1 1 1 1 1 1 1 X 0 X X^2 0 X X X 1 X X^2 X^2 X^2 1 X 1 0 0 1 0 X 0 0 0 0 0 0 0 0 X^2 X X X^2+X 0 X^2+X X^2+X 0 X X^2 X^2+X X^2 X X X X^2 X 0 X X^2 X^2+X X X^2+X X^2+X X^2+X X^2+X X 0 X X^2 X^2 X^2 0 0 X^2+X X X X^2 X 0 0 X^2 X^2+X X X^2+X X X^2 0 X^2 0 X^2 0 0 X^2 0 0 X 0 0 0 0 0 0 0 X^2+X X^2 X X X X 0 X 0 X X^2+X X^2 0 X^2+X X X X^2+X X^2+X X^2 0 X^2+X 0 X^2 X^2+X X 0 X^2 X^2+X X^2+X X^2 X X^2+X X^2 X^2 0 X^2 X 0 0 X X^2+X 0 X^2 X^2 X^2+X 0 X 0 X^2 X X^2+X X 0 X^2+X 0 0 0 X 0 0 0 X X^2+X X X X^2+X 0 X X^2 0 X^2+X X^2+X X^2+X X^2 X^2+X X 0 X^2 0 X^2 X X X X^2 X 0 X^2+X 0 X X^2+X 0 X^2 X^2+X X^2 X X 0 X^2 X X X X X^2+X X^2 X^2+X X X X^2 X X 0 X X^2 0 X^2+X X^2+X X X^2 0 0 0 0 X 0 X X X X^2 X X X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X X^2+X X^2 X^2 X 0 X^2+X X^2 X^2+X X^2+X X X^2+X X 0 X^2+X X^2+X X^2+X 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2 X 0 X X 0 X 0 X^2+X X^2+X X^2 X^2+X X^2 X^2 X^2 X X 0 0 0 0 0 X X X^2 X^2+X X^2+X X X X^2+X 0 X X^2 X^2 X^2 X^2+X X 0 X^2 X^2 0 X 0 X X^2 X^2 X^2+X X^2+X X^2+X X^2+X 0 X^2 X^2 X^2 X X^2+X X^2 X X^2 X^2 X X^2+X 0 X 0 X^2+X X^2 X^2 X X^2+X X^2+X X X^2+X X^2 X 0 X X X^2+X X X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 53. Homogenous weight enumerator: w(x)=1x^0+82x^53+181x^54+234x^55+362x^56+422x^57+485x^58+606x^59+899x^60+1100x^61+1386x^62+1616x^63+1627x^64+1702x^65+1362x^66+1184x^67+866x^68+578x^69+517x^70+342x^71+286x^72+178x^73+139x^74+98x^75+51x^76+32x^77+20x^78+16x^79+4x^80+2x^81+5x^82+1x^98 The gray image is a linear code over GF(2) with n=256, k=14 and d=106. This code was found by Heurico 1.16 in 29.7 seconds.