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 X^2  1  1  1  1  1  1  1 X^3+X^2  1  1  X  1  1  1  X  1  1  1  X  1 X^2  1 X^3+X^2  1  1  X  0  1  1  X  1  1  1  1  X
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2+X X^3+X^2  X X^3+X^2 X^2+X X^2+X X^3+X^2 X^3+X^2+X X^3+X X^3+X^2 X^2 X^3+X X^3+X^2 X^3+X X^3  0 X^2+X X^3 X^2+X X^3+X^2 X^3+X  0  X X^2 X^3+X X^2+X  X X^3+X^2+X X^3+X  0  X X^3+X^2+X X^3+X^2  X X^3+X  X X^2+X  X X^3 X^3+X^2+X X^3+X  X X^3+X^2+X X^2  X X^3 X^2 X^3+X^2 X^3+X^2+X  0
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2  X  X X^3+X^2+X X^3+X  0 X^3  X  0 X^3+X X^2  0 X^3 X^2+X  X X^2+X X^2 X^3 X^3+X X^3+X^2+X X^3+X^2  X X^3 X^3+X^2+X X^2 X^2 X^3+X X^3+X^2 X^3+X X^3+X X^2+X X^3 X^2 X^3+X^2+X X^2 X^3+X X^3+X^2+X X^3+X^2+X X^2 X^3+X^2  0 X^3+X^2 X^3+X X^3+X^2 X^2 X^2+X X^3+X  X X^2 X^2+X
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2  0 X^2  0 X^2  0  0 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2  0  0 X^2 X^3 X^3 X^2 X^2  0 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^3  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3 X^2  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+246x^58+16x^59+629x^60+192x^61+900x^62+352x^63+808x^64+192x^65+424x^66+16x^67+191x^68+84x^70+34x^72+10x^74+1x^104

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 0.547 seconds.