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 X^2 1 1 X X X X 1 1 X^2 X X 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 X^2+X X^2 X^2 X^2+X X X X^2+X 0 0 0 X 0 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 0 X X^2+X X X X^2 0 X^2 X^2+X 0 0 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 X^2 X^2 X^2 X^2 X X^2+X X X^2 X 0 0 0 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 X^2+X 0 X X^2+X X X X^2+X X^2+X X^2+X 0 0 X^2+X X 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 0 0 0 X^2 X^2 0 0 0 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 0 0 X^2 0 0 0 0 X^2 0 X^2 0 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+88x^54+373x^56+36x^57+601x^58+152x^59+711x^60+320x^61+885x^62+488x^63+979x^64+536x^65+877x^66+360x^67+646x^68+128x^69+443x^70+24x^71+285x^72+4x^73+148x^74+70x^76+28x^78+5x^80+2x^82+1x^84+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 5.7 seconds.