The generator matrix

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

generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+429x^58+1158x^59+2048x^60+2644x^61+4213x^62+3710x^63+4757x^64+3974x^65+3761x^66+2586x^67+1772x^68+824x^69+485x^70+162x^71+134x^72+30x^73+54x^74+16x^75+8x^76+2x^78

The gray image is a linear code over GF(2) with n=512, k=15 and d=232.
This code was found by Heurico 1.16 in 12.8 seconds.