The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1  2 2X+2  0  1  1 X+2 X+2  1  1 3X 3X+2 3X  1  1 2X+2  1  1  1 3X  1  2  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1 3X  1
 0  1  0 2X  3 2X+3  1  X X+3 3X 3X+3  1  X  1 3X+1  0  1  X  2 2X+1  1  1  1 X+2  X  1 X+3 3X+1  2  2 2X+3  1 3X+2 3X X+2  1 2X  3 3X+1 2X+2 X+2  1 2X+1 3X+3  2  X X+2 2X+2  0 X+1  1 2X
 0  0  1 3X+1 X+1 2X X+1  X 2X+1  1 3X 3X  1  3  2 3X+2 X+2  1  3 2X+1 2X+3 2X+2 X+3 3X+3  0 X+1 X+1 X+2 2X  1 3X 2X+1 2X+2 3X+1  X 2X+2  1  3 2X X+3 X+1 3X+3 3X+2  3 2X+2 2X+3 2X+1 3X+1  X 3X+1 3X 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+48x^48+514x^49+758x^50+634x^51+660x^52+494x^53+340x^54+210x^55+194x^56+164x^57+45x^58+28x^59+4x^61+1x^66+1x^72

The gray image is a code over GF(2) with n=416, k=12 and d=192.
This code was found by Heurico 1.16 in 0.156 seconds.