The generator matrix

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

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+166x^56+646x^57+1004x^58+1234x^59+1547x^60+2230x^61+2447x^62+2758x^63+2720x^64+3132x^65+2932x^66+2946x^67+2456x^68+2168x^69+1535x^70+1140x^71+707x^72+462x^73+258x^74+144x^75+79x^76+18x^77+16x^78+18x^79+4x^80

The gray image is a linear code over GF(2) with n=260, k=15 and d=112.
This code was found by Heurico 1.13 in 13.5 seconds.