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  0  1  1  X  X  1  1 X^2  X  1  X  1  1  0  1  0  1 X^2 X^2  1  0  1  1  1  1  0  1  X  1  1  X  1  1
 0  X  0  0  0  0  0  0 X^2  X X^2+X X^2+X  X  X  X  X X^2  0 X^2 X^2  X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2  X  0  0 X^2+X  X X^2+X X^2+X X^2  0 X^2  X  X X^2+X X^2+X  0  0 X^2 X^2 X^2  X  0  0  X  X  0 X^2  0 X^2  0  0 X^2+X X^2  0 X^2
 0  0  X  0  0  0  X X^2+X X^2+X  X  X X^2  X  X X^2+X  0 X^2 X^2 X^2+X  X X^2  X  0 X^2  X X^2  0  X  0  X  0 X^2+X X^2 X^2+X  X  X X^2+X  0  X X^2  X X^2+X X^2 X^2 X^2  X  X  X  0  0 X^2 X^2  0  0  0 X^2 X^2+X  X  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X X^2  0 X^2+X X^2 X^2+X  0 X^2+X X^2 X^2 X^2+X  X  0 X^2+X X^2  X X^2+X  0 X^2+X  X X^2+X X^2  X  X  0  0  X  X X^2+X X^2+X  0  0 X^2 X^2+X  0  X  X X^2+X  0 X^2  X X^2  X  0  0  X X^2+X X^2  0  X X^2+X  0
 0  0  0  0  X  X X^2 X^2+X  X X^2  X  0  X  0  X  0 X^2  0  X X^2+X X^2+X X^2  X X^2  X X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2  0 X^2+X X^2  X X^2  0  X  X X^2 X^2 X^2+X  0 X^2+X  X X^2 X^2 X^2+X X^2  X X^2 X^2 X^2+X X^2 X^2+X  0  0  X  X  0 X^2+X  X
 0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  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+51x^56+70x^57+92x^58+228x^59+152x^60+330x^61+134x^62+584x^63+124x^64+694x^65+105x^66+588x^67+95x^68+310x^69+100x^70+148x^71+64x^72+60x^73+63x^74+48x^75+21x^76+8x^77+17x^78+4x^79+4x^80+1x^102

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 1.3 seconds.