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  X  1  1  1  1  X
 0  X  0 X+2  2 3X+2 2X+2  X  0 X+2 2X 3X  X 2X+2 2X+2 X+2  0 X+2 2X+2 3X 2X X+2 2X X+2 3X+2  2  0 3X 3X 2X 3X+2 2X 2X 3X 2X+2 X+2  X 3X 2X 2X 2X+2 2X+2 2X+2 2X X+2  2 3X+2  2 2X  0 3X+2 3X+2
 0  0 2X+2  0  2  2  0  2  0  0  2  2 2X  2 2X 2X+2 2X 2X 2X+2 2X+2  2 2X+2 2X  0 2X+2  2 2X  0 2X+2 2X+2  0  0  2 2X 2X+2 2X+2  2 2X+2 2X  0 2X+2  0 2X 2X+2 2X  2 2X+2 2X+2 2X+2  2 2X+2  2
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X  0  0  0 2X  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X
 0  0  0  0 2X  0 2X  0 2X 2X 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0  0 2X  0 2X  0 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X  0  0  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+223x^48+192x^50+1219x^52+192x^54+216x^56+4x^60+1x^100

The gray image is a code over GF(2) with n=416, k=11 and d=192.
This code was found by Heurico 1.16 in 0.36 seconds.