The generator matrix

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

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+466x^59+1152x^60+2088x^61+2967x^62+3952x^63+3865x^64+4212x^65+4166x^66+3628x^67+2422x^68+1946x^69+1044x^70+474x^71+198x^72+88x^73+42x^74+22x^75+10x^76+18x^77+5x^78+2x^79

The gray image is a linear code over GF(2) with n=520, k=15 and d=236.
This code was found by Heurico 1.16 in 44.8 seconds.