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

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+64x^55+119x^56+194x^57+222x^58+336x^59+386x^60+418x^61+593x^62+684x^63+784x^64+760x^65+797x^66+670x^67+507x^68+428x^69+317x^70+268x^71+180x^72+146x^73+89x^74+80x^75+63x^76+34x^77+29x^78+8x^79+8x^80+4x^81+2x^83+1x^94

The gray image is a linear code over GF(2) with n=260, k=13 and d=110.
This code was found by Heurico 1.16 in 5.44 seconds.