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

generates a code of length 52 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+47x^48+928x^52+47x^56+1x^104

The gray image is a code over GF(2) with n=416, k=10 and d=192.
This code was found by Heurico 1.16 in 0.093 seconds.