The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1  1  1  1  1  1  1  1  1
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^2+X X^3+X^2  X X^2 X^3+X X^2 X^2+X  0 X^3+X^2+X X^2 X^3+X^2+X X^3 X^2+X X^3  X  0 X^3+X  0 X^2+X X^3+X X^3+X^2 X^3  X X^3  X X^3+X X^3+X^2 X^3+X^2 X^2+X  X X^3 X^3+X^2+X X^3+X^2 X^3+X^2 X^2+X X^3+X X^3+X^2 X^3+X^2  X X^2+X X^2+X X^3+X^2+X  X  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2+X X^3+X X^2+X  X  0  0  0  0
 0  0 X^3+X^2  0  0 X^3+X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^3 X^3+X^2  0 X^2 X^3  0 X^3+X^2 X^2 X^2  0 X^3  0 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^2  0 X^2 X^3 X^2 X^2 X^3  0 X^2 X^3 X^3+X^2  0 X^3 X^3+X^2 X^3 X^2  0 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2  0
 0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^3 X^2 X^2 X^2 X^2  0 X^3 X^3 X^3  0  0 X^3+X^2  0  0 X^3+X^2 X^2 X^2 X^2 X^2 X^2 X^3+X^2  0  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+64x^61+160x^62+64x^63+958x^64+544x^66+64x^69+128x^70+64x^71+1x^128

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 0.312 seconds.