The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^51+85x^52+7x^56+4x^59+3x^60

The gray image is a code over GF(2) with n=416, k=7 and d=204.
This code was found by Heurico 1.16 in 0.063 seconds.