The generator matrix

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

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+610x^50+2052x^51+3761x^52+5488x^53+7476x^54+8592x^55+9787x^56+8700x^57+7744x^58+5288x^59+3180x^60+1728x^61+682x^62+216x^63+138x^64+52x^65+22x^66+12x^67+5x^68+2x^70

The gray image is a code over GF(2) with n=448, k=16 and d=200.
This code was found by Heurico 1.16 in 30.2 seconds.