The generator matrix

 1  0  0  1  1  1  X  0  1  1  1  X X^2+X  1 X^2  1  0  X  1  1  1 X^2+X  1  0  1  X  1  1  0  1  1  1 X^2+X  1 X^2+X X^2  1  1  1  1  X  1  1  X  1  X  X  0  1  X  X X^2+X  1  1  1  X  1  0  1  1  1 X^2 X^2  1 X^2
 0  1  0  0  1 X^2+X+1  1  1  X X+1  1 X^2+X  1  X X^2+X  1  1  1  X X^2+1  X  1 X^2+X+1 X^2  0  1 X+1 X^2+1  1 X^2  0 X^2+X X^2 X^2+1  1  1  1 X^2  0  0  1 X^2+X  1  1  1  1 X^2 X^2+X X^2+X+1 X^2  1  1 X^2+X+1  X X^2+X  1  X  1  0 X^2+1 X+1  1  1 X^2+1  0
 0  0  1  1  1  0  1 X+1 X+1  X X^2+X+1  1  X  X  1  X X^2+X+1  X  1 X^2+1 X^2+X X+1  X  1 X^2+1  0 X^2+X+1 X+1  1  0 X+1 X^2  1 X+1  X  0 X^2  1 X^2 X^2+1  1  X X^2  1 X^2  0  1  1 X^2+1  1 X^2+X+1 X^2  X  X X^2+1 X^2+X  1  X X^2+X+1  1 X^2 X^2+X  X  0  X
 0  0  0  X  0 X^2+X X^2  0  X X^2+X  0  0 X^2+X X^2 X^2+X X^2 X^2+X  0 X^2  X X^2+X  X  0 X^2+X  0  X X^2 X^2+X X^2+X  X  X X^2  X X^2  0  X  0 X^2+X X^2+X X^2 X^2  0 X^2+X  X  0  0 X^2  0  X  0 X^2 X^2+X X^2+X X^2+X  X X^2  0 X^2 X^2+X  0  X X^2  0  0 X^2+X
 0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  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+395x^58+992x^60+1386x^62+1565x^64+1330x^66+1181x^68+725x^70+373x^72+180x^74+39x^76+13x^78+9x^80+3x^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 1.16 in 30.1 seconds.