The generator matrix

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

generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+115x^56+998x^57+2288x^58+3950x^59+5582x^60+7164x^61+8284x^62+8936x^63+8541x^64+7260x^65+5395x^66+3594x^67+1863x^68+918x^69+370x^70+174x^71+53x^72+26x^73+15x^74+5x^76+2x^77+2x^79

The gray image is a linear code over GF(2) with n=504, k=16 and d=224.
This code was found by Heurico 1.16 in 33.5 seconds.