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

generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+40x^60+192x^61+79x^62+880x^63+63x^64+528x^65+16x^66+16x^67+24x^68+176x^69+32x^70+1x^126

The gray image is a linear code over GF(2) with n=512, k=11 and d=240.
This code was found by Heurico 1.16 in 0.312 seconds.