The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+27x^50+48x^51+59x^52+78x^53+112x^54+408x^55+654x^56+394x^57+102x^58+42x^59+24x^60+28x^61+26x^62+12x^63+9x^64+10x^65+2x^66+2x^67+5x^68+2x^69+2x^70+1x^98

The gray image is a code over GF(2) with n=448, k=11 and d=200.
This code was found by Heurico 1.16 in 0.219 seconds.