The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+244x^52+128x^53+344x^54+128x^55+130x^56+24x^58+24x^60+1x^96

The gray image is a code over GF(2) with n=432, k=10 and d=208.
This code was found by Heurico 1.16 in 0.125 seconds.