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

generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+63x^62+896x^63+63x^64+1x^126

The gray image is a linear code over GF(2) with n=504, k=10 and d=248.
This code was found by Heurico 1.16 in 0.313 seconds.