The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^50+94x^52+96x^53+156x^54+416x^55+432x^56+416x^57+122x^58+96x^59+65x^60+64x^62+14x^64+8x^66+1x^72+1x^100

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 63.8 seconds.