The generator matrix

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

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+138x^56+32x^57+240x^58+144x^59+601x^60+352x^61+668x^62+624x^63+968x^64+768x^65+876x^66+624x^67+746x^68+352x^69+468x^70+144x^71+294x^72+32x^73+52x^74+33x^76+17x^80+12x^84+6x^88

The gray image is a linear code over GF(2) with n=260, k=13 and d=112.
This code was found by Heurico 1.16 in 4.15 seconds.