The generator matrix

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

generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+180x^59+123x^60+380x^61+132x^62+460x^63+146x^64+312x^65+88x^66+188x^67+17x^68+12x^69+2x^70+4x^71+1x^72+2x^86

The gray image is a linear code over GF(2) with n=504, k=11 and d=236.
This code was found by Heurico 1.16 in 0.36 seconds.