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  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 2X  0  0  0  0  0  0  0 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0  0  0  0  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0 2X  0 2X
 0  0 2X  0  0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0
 0  0  0 2X  0  0  0  0 2X  0  0 2X  0 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0  0  0  0 2X  0  0 2X 2X 2X  0  0
 0  0  0  0 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X 2X 2X  0  0  0 2X  0  0 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0
 0  0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X  0
 0  0  0  0  0  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0  0 2X 2X  0  0  0  0 2X  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X
 0  0  0  0  0  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X  0 2X 2X

generates a code of length 63 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+50x^56+65x^58+256x^62+1280x^63+307x^64+36x^66+26x^72+26x^74+1x^122

The gray image is a code over GF(2) with n=504, k=11 and d=224.
This code was found by Heurico 1.16 in 0.266 seconds.