The generator matrix

 1  0  0  0  1  1  1  X X^2  1  1  0 X^2  1  1  1 X^2+X X^2 X^2+X  1  1  1  1  X  0 X^2+X  1 X^2+X  1  X  1 X^2  1  1  1  1 X^2+X  1  1 X^2  1  0 X^2  X  1  0  1  1  1  X  1 X^2+X X^2+X  X X^2+X  1  1  0  1  1  1  1  1  X  1
 0  1  0  0  1 X^2  1  1  0  1 X^2  1  1  X  1 X^2+X  1  X  1 X+1 X^2+X X^2+X+1 X^2+1  0  1  1 X^2+X+1  X  1 X^2 X^2  X  X X^2  0  0 X^2+X X^2+X+1 X+1 X^2+X X^2+X  X  1  0  0  1 X^2+X+1  1 X^2+X X^2+X  1  1  1  1  1  0 X^2+1  1 X^2  0 X^2+1 X^2+X  0  1  0
 0  0  1  0  X  0 X^2+X X^2  1 X^2+X+1  1 X^2+X+1 X^2+X+1  1 X^2+1 X+1  1  1 X^2  0 X^2+X  X  1 X^2+X  0 X^2+X+1  0  1 X+1  1 X^2+X+1  1 X^2  X X^2+X X+1  1 X^2  X X^2  1  1  X  1 X+1  X X^2+X+1  0 X^2+X+1  0 X^2+X+1 X^2+X+1 X+1 X+1 X^2+1 X^2+X+1 X^2  1  0 X+1  0  X X^2+1  X  1
 0  0  0  1  X  1 X+1  1  1 X^2+1 X^2+X X^2+X X+1 X+1 X^2  0 X^2+1  0 X^2+X+1 X^2+X X^2+X X^2+X+1  X  1  X  0 X^2+1 X^2+X+1 X^2 X^2 X+1  1  1  1 X^2 X^2 X^2+X  0  X  1 X^2+X+1  1  0 X^2+1 X^2+X X^2+X+1 X^2+1 X^2+X  X  1 X^2+X+1 X^2+1  1  X X^2+X+1 X^2  0 X^2+1 X+1 X^2+X+1 X^2  0 X^2 X+1 X^2+1
 0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+187x^58+388x^59+575x^60+544x^61+737x^62+776x^63+828x^64+672x^65+704x^66+520x^67+559x^68+516x^69+397x^70+272x^71+246x^72+112x^73+73x^74+28x^75+28x^76+12x^77+12x^78+3x^80+2x^82

The gray image is a linear code over GF(2) with n=260, k=13 and d=116.
This code was found by Heurico 1.11 in 1.06 seconds.