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  2  1  1  1  2  2  2
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 3X 2X+2 2X 3X+2  2 3X  0 X+2 2X+2 3X  0 X+2 3X 2X+2 X+2  0 2X+2 3X  0 2X+2 X+2 3X 2X 3X+2  2 3X+2 2X  X  2  X  0  0 2X 2X X+2 2X+2 3X+2 X+2 3X+2 2X+2 2X+2 2X+2
 0  0 2X  0  0  0 2X  0  0  0  0 2X  0  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0  0  0  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0
 0  0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0  0  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X  0  0  0 2X  0 2X  0  0  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0  0
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0 2X 2X 2X  0  0  0 2X  0  0  0 2X 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+352x^48+1352x^52+332x^56+8x^60+2x^64+1x^96

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 0.671 seconds.