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

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+112x^59+181x^60+296x^61+293x^62+392x^63+297x^64+236x^65+61x^66+68x^67+41x^68+44x^69+12x^70+4x^71+8x^72+1x^74+1x^110

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 0.312 seconds.