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

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+105x^58+8x^59+183x^60+64x^61+261x^62+132x^63+267x^64+116x^65+293x^66+112x^67+182x^68+72x^69+59x^70+4x^71+97x^72+4x^73+42x^74+31x^76+8x^78+6x^80+1x^104

The gray image is a linear code over GF(2) with n=260, k=11 and d=116.
This code was found by Heurico 1.16 in 0.461 seconds.