The generator matrix

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

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+667x^60+776x^61+2066x^62+1552x^63+2838x^64+1520x^65+2468x^66+1136x^67+1537x^68+760x^69+662x^70+128x^71+175x^72+16x^73+48x^74+28x^76+4x^78+2x^80

The gray image is a linear code over GF(2) with n=520, k=14 and d=240.
This code was found by Heurico 1.16 in 638 seconds.