The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+25x^52+4x^54+2x^58

The gray image is a code over GF(2) with n=408, k=5 and d=208.
This code was found by Heurico 1.16 in 0.046 seconds.