The generator matrix

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

generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+314x^60+392x^61+372x^62+96x^63+314x^64+224x^65+216x^66+49x^68+56x^69+4x^70+8x^76+1x^80+1x^84

The gray image is a linear code over GF(2) with n=504, k=11 and d=240.
This code was found by Heurico 1.16 in 0.187 seconds.