The generator matrix

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

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+43x^50+166x^51+154x^52+470x^53+262x^54+774x^55+374x^56+858x^57+293x^58+368x^59+89x^60+134x^61+33x^62+32x^63+16x^64+6x^65+8x^66+2x^67+5x^68+4x^69+1x^70+2x^71+1x^88

The gray image is a code over GF(2) with n=448, k=12 and d=200.
This code was found by Heurico 1.16 in 0.469 seconds.