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 X X X X X 0 1 1 X 1 X X 1 X 1 X^2 X X^2 X^2 1 X 1 1 1 1 X X^2 1 X^2 1 1 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X X X 0 0 0 X^2 X^2+X X^2+X X^2 X^2+X X X^2+X 0 0 X^2+X X 0 X X^2 X 0 X X 0 X^2+X X 0 0 X^2 X X^2 X X^2 X X^2 X X X X X X^2 0 X^2 X^2+X 0 X^2 X X^2 0 X^2 X 0 0 0 X 0 X X X^2+X 0 0 0 X X X 0 X^2 X^2+X X 0 X^2 X^2 0 0 X^2+X X^2 X X^2+X X^2 X^2+X 0 X^2+X X X^2+X X X X^2+X 0 0 X^2 X^2 X^2 0 X X 0 0 X^2 X^2+X 0 0 X^2+X X X^2+X X X^2+X 0 X^2+X X^2+X X^2+X X X^2 0 X X^2+X X 0 0 0 0 X X 0 X^2+X X X^2 X X^2 0 X X^2 X^2+X X X^2 X^2 X X^2+X X^2 X 0 X X^2+X X^2+X 0 X^2+X 0 0 0 X^2+X X^2+X X^2+X 0 X^2+X X^2+X 0 0 X^2+X X^2+X 0 X^2+X X X^2+X 0 X^2 X^2 X 0 0 X 0 0 X^2 X^2 0 X^2 X^2+X X^2 X^2+X X^2 X X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 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 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 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 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+35x^54+64x^55+133x^56+160x^57+264x^58+326x^59+354x^60+420x^61+532x^62+668x^63+761x^64+828x^65+750x^66+694x^67+548x^68+442x^69+329x^70+242x^71+169x^72+170x^73+100x^74+44x^75+66x^76+26x^77+31x^78+10x^79+16x^80+2x^81+6x^82+1x^94 The gray image is a linear code over GF(2) with n=260, k=13 and d=108. This code was found by Heurico 1.16 in 5.74 seconds.