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

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+144x^56+156x^58+444x^60+540x^62+813x^64+740x^66+605x^68+308x^70+218x^72+48x^74+48x^76+22x^80+6x^84+2x^88+1x^100

The gray image is a linear code over GF(2) with n=260, k=12 and d=112.
This code was found by Heurico 1.16 in 94.2 seconds.