The generator matrix

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

generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+83x^58+298x^59+348x^60+612x^61+469x^62+626x^63+500x^64+442x^65+269x^66+250x^67+108x^68+64x^69+7x^70+4x^71+2x^72+2x^73+2x^74+6x^79+1x^80+2x^82

The gray image is a linear code over GF(2) with n=504, k=12 and d=232.
This code was found by Heurico 1.16 in 0.421 seconds.