The generator matrix

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

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+665x^56+2134x^57+4475x^58+7280x^59+10553x^60+14782x^61+15996x^62+18732x^63+16906x^64+15076x^65+10747x^66+6996x^67+3715x^68+1672x^69+772x^70+356x^71+128x^72+30x^73+41x^74+12x^75+2x^77+1x^82

The gray image is a linear code over GF(2) with n=504, k=17 and d=224.
This code was found by Heurico 1.16 in 469 seconds.