The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+380x^50+260x^52+380x^54+2x^68+1x^72

The gray image is a code over GF(2) with n=416, k=10 and d=200.
This code was found by Heurico 1.16 in 0.563 seconds.