The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+304x^48+384x^49+512x^50+640x^51+438x^52+640x^53+512x^54+384x^55+256x^56+18x^60+5x^64+2x^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 0.375 seconds.