The generator matrix

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

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+156x^61+164x^62+392x^63+124x^64+368x^65+248x^66+304x^67+64x^68+172x^69+34x^70+8x^71+2x^72+8x^73+1x^78+1x^80+1x^94

The gray image is a linear code over GF(2) with n=520, k=11 and d=244.
This code was found by Heurico 1.16 in 0.203 seconds.