The generator matrix

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

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+118x^61+572x^62+606x^63+896x^64+468x^65+416x^66+254x^67+253x^68+174x^69+185x^70+64x^71+65x^72+12x^73+10x^74+1x^80+1x^82

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 6.81 seconds.