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

generates a code of length 63 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+88x^52+156x^53+227x^54+354x^55+331x^56+478x^57+610x^58+878x^59+1016x^60+1398x^61+1847x^62+1672x^63+1812x^64+1436x^65+1109x^66+854x^67+499x^68+532x^69+325x^70+224x^71+184x^72+142x^73+85x^74+44x^75+33x^76+18x^77+20x^78+6x^79+4x^80+1x^102

The gray image is a code over GF(2) with n=252, k=14 and d=104.
This code was found by Heurico 1.16 in 19.4 seconds.