The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+312x^49+1750x^50+3608x^51+7042x^52+10600x^53+14618x^54+17622x^55+19435x^56+18292x^57+15404x^58+10280x^59+6643x^60+3150x^61+1422x^62+550x^63+216x^64+88x^65+20x^66+4x^67+7x^68+6x^69+2x^74

The gray image is a code over GF(2) with n=448, k=17 and d=196.
This code was found by Heurico 1.16 in 119 seconds.