The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X^2+X  1 X^3+X^2  1  1 X^3+X  1 X^2  X  1  1  1  1  0 X^2+X  1  1  1  1  1  1 X^3+X^2 X^3+X  1  1  1  1 X^3  1  1 X^3+X^2+X  1  1  1 X^2  X  1  X  1  1  1  1 X^3 X^3+X^2+X X^3+X^2  1  1  1  X  X  1  0 X^3+X^2  X
 0  1 X+1 X^2+X X^2+1  1 X^3+1 X^3  1 X^2+X+1 X^3+X^2+X  1 X^2  1 X^3+X^2+1  X  1 X+1  1  1 X^3+X^2+X+1 X^3+X^2 X^3+X  1  1  1 X^3+X+1  1  0 X^3+X X^2+X+1 X^3+X^2+1  1  1 X^3+X^2 X^2+X X+1  0  1 X^3+X^2 X^2+1  1 X^2+X X^3+X X^3+1  1  1 X^3+X^2+X+1 X^2+X X^2+1 X^3+1 X^3+X+1 X^3+X+1  1  1  1 X^3+X^2+X  0 X^3+X^2+X  1 X^2 X^3+X  X  X  0
 0  0 X^2  0 X^3  0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^3 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2 X^3 X^3 X^3  0  0 X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3  0  0  0 X^3+X^2 X^2  0
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 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+154x^61+186x^62+282x^63+330x^64+236x^65+276x^66+208x^67+192x^68+134x^69+34x^70+6x^71+2x^72+2x^73+3x^80+2x^89

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 0.297 seconds.