The generator matrix

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

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+200x^58+1046x^59+2288x^60+4000x^61+5628x^62+7034x^63+8021x^64+9284x^65+8524x^66+7182x^67+4986x^68+3488x^69+2088x^70+1006x^71+426x^72+212x^73+68x^74+20x^75+22x^76+8x^77+4x^78

The gray image is a linear code over GF(2) with n=520, k=16 and d=232.
This code was found by Heurico 1.16 in 34.1 seconds.