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

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+191x^60+16x^61+316x^62+368x^63+339x^64+368x^65+240x^66+16x^67+127x^68+52x^70+12x^72+1x^76+1x^116

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 0.297 seconds.