The generator matrix

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

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+8x^50+32x^51+174x^52+30x^53+7x^54+1x^56+2x^69+1x^70

The gray image is a code over GF(2) with n=416, k=8 and d=200.
This code was found by Heurico 1.16 in 0.094 seconds.