The generator matrix

 1  0  1  1  1 X+2  1  1 2X  1  1 3X+2  1 2X+2  1  1  X  1  1  1 2X  X  1  1  2 3X 2X X+2  X 2X+2 3X+2 2X  1  1  1  1 3X+2  0  1  1  1  1  1  X  1  0 2X+2  1  1  1  1  1
 0  1 X+1 X+2  3  1 2X+1 2X  1 X+3 3X+2  1  2  1 2X+3 3X  1 X+1  1 2X+2  1  1 3X+3  X  1  1  1  1  1  1  1  1  0 X+2  0  2  1  1 X+2 X+1 X+3 X+2  X 3X+2 3X+2  1  1  0 3X 3X+2  0 2X
 0  0  2  0 2X  0 2X  2  2 2X+2 2X+2 2X+2  2  0 2X+2 2X  2  0  2 2X 2X 2X+2  0 2X+2  2 2X  2  0 2X 2X 2X+2 2X+2  0 2X  2 2X+2 2X 2X+2  2 2X 2X+2 2X  2  2 2X+2 2X 2X 2X  0  0 2X 2X
 0  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0 2X 2X  0  0 2X  0 2X 2X  0  0 2X  0  0 2X  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0

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+51x^48+254x^49+273x^50+344x^51+271x^52+302x^53+229x^54+232x^55+58x^56+18x^57+8x^58+3x^60+2x^61+1x^62+1x^82

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 0.156 seconds.