The generator matrix

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

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+360x^61+417x^62+652x^63+405x^64+568x^65+446x^66+496x^67+374x^68+244x^69+17x^70+72x^71+1x^72+28x^73+12x^75+1x^80+2x^88

The gray image is a linear code over GF(2) with n=520, k=12 and d=244.
This code was found by Heurico 1.16 in 0.438 seconds.