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  X  1  1  1  1  1  1  1  1 2X+2  1  1  1  1  1  1  1  X 2X+2  1
 0  2  0  2  0  2  0 2X+2 2X  2  0  2  2  0 2X 2X+2 2X 2X+2 2X+2  0  0 2X  2  2  0  2  2  0  2 2X+2  2  0 2X  0 2X  2  0  2 2X+2 2X+2  0 2X  2 2X+2 2X 2X 2X  0 2X 2X 2X+2 2X+2  2  2  0  2
 0  0 2X  0  0  0  0  0 2X  0  0 2X 2X 2X 2X  0 2X 2X 2X  0 2X  0  0  0  0  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X  0 2X 2X
 0  0  0 2X  0  0  0 2X  0  0  0 2X  0  0  0 2X  0  0 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0 2X 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X
 0  0  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X 2X  0 2X  0  0 2X 2X 2X  0 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X 2X 2X 2X  0
 0  0  0  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X  0 2X 2X  0 2X 2X  0  0  0  0  0  0 2X 2X  0 2X 2X 2X  0  0  0 2X  0  0 2X 2X  0  0 2X
 0  0  0  0  0  0 2X  0 2X  0 2X  0  0  0 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X 2X 2X  0  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+57x^50+81x^52+64x^53+99x^54+128x^55+1256x^56+64x^57+185x^58+29x^60+33x^62+34x^64+10x^66+6x^68+1x^104

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 0.328 seconds.