The generator matrix

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

generates a code of length 50 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+20x^51+5x^52+4x^53+2x^54

The gray image is a code over GF(2) with n=400, k=5 and d=204.
This code was found by Heurico 1.16 in 0.063 seconds.