The generator matrix

 1  0  0  1  1  1 X^3  1  1 X^3+X^2+X X^2+X  1 X^2+X  1  1 X^3+X^2 X^3+X X^2+X  1  1  1  0 X^3+X^2+X  1  1  1 X^3+X^2  1  1  1 X^2  1  1 X^3+X^2+X X^3+X^2  1  1 X^3+X^2+X  1  1  X  1 X^3+X^2 X^2+X  1  1 X^2  1  1  1  1  0 X^3+X^2 X^2+X  X  1 X^3+X  1 X^3  1 X^2  0 X^3+X^2  X  1
 0  1  0 X^2 X^3+X^2+1 X^2+1  1 X^3+X X^3+X^2+X+1  1  1 X^2  0 X^3+X+1 X^3  1  1  X X+1  1 X^2+X X^2+X  1 X^3+X^2+X+1  X  1  1 X^3+X^2 X^3 X^3+1  1 X^3+X^2+X X^3+X+1  1 X^3 X^3+1  0  1 X^3+X^2+X X^3+X+1  1 X^2  X  1 X^2+X+1 X^3+1  1  X X^3+X X^2+1 X^3+X  1  1  1  1 X^2+X+1 X^3+X X^2+1  1 X^2+X  1  1 X^3  1  0
 0  0  1 X^2+X+1 X^3+X^2+X+1 X^3+X^2 X^3+X+1 X^2+X X^2+1 X^2+X+1 X^2  1  1 X^3+X^2 X^3+X^2+X X^3+X^2+X  1  1 X+1  X X^3+X^2+1  1 X^3+X  X X^3 X^3+1  1 X+1 X^2 X^2+X+1 X^2+1 X^3+X+1 X^3+X^2+X+1 X^3  1 X^2  1 X^3+1  X X^3 X^3+X X^2+X  1 X^2+X X^2+1 X^2+X X^3+X^2+X  0 X^3+X+1 X^3+X^2+1  1 X^3 X+1 X^3+X+1 X+1 X+1  1 X^3+X^2  X X^3+X^2 X^2+1  1  1 X^2+X+1  0
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0  0  0

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+98x^60+554x^61+866x^62+1346x^63+1096x^64+1208x^65+708x^66+824x^67+439x^68+462x^69+231x^70+162x^71+124x^72+44x^73+18x^74+4x^75+1x^76+4x^77+1x^78+1x^80

The gray image is a linear code over GF(2) with n=520, k=13 and d=240.
This code was found by Heurico 1.16 in 1.83 seconds.