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

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

Homogenous weight enumerator: w(x)=1x^0+290x^48+448x^52+280x^56+4x^64+1x^96

The gray image is a code over GF(2) with n=208, k=10 and d=96.
This code was found by Heurico 1.16 in 99.6 seconds.