The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 0 1 1 X^2+X 1 1 1 0 1 X^2+X 1 1 1 1 0 1 1 X^2+X 1 1 1 1 X^2+X 0 1 1 0 0 1 1 X^2+X X^2 X^2+X 1 1 1 1 1 1 1 1 1 X 1 1 1 X^2+X X^2 X^2+X 1 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 1 0 X^2+1 1 X^2+X X+1 X 1 X+1 1 X^2+1 0 X^2 X+1 1 X^2+X X+1 1 X^2+1 0 X^2+1 X^2+X 1 1 X^2+1 X+1 1 1 0 X^2+X+1 1 1 1 X^2+X X^2+X X+1 0 X^2+X 0 1 X+1 X^2+X+1 1 X^2+X+1 X 0 1 1 1 0 X+1 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 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 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 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 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+41x^54+36x^55+99x^56+184x^57+331x^58+252x^59+631x^60+468x^61+935x^62+596x^63+1136x^64+596x^65+906x^66+468x^67+592x^68+252x^69+290x^70+184x^71+70x^72+36x^73+35x^74+19x^76+11x^78+5x^80+8x^82+6x^84+3x^86+1x^88 The gray image is a linear code over GF(2) with n=256, k=13 and d=108. This code was found by Heurico 1.16 in 4.14 seconds.