The generator matrix

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

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+265x^50+960x^51+1779x^52+3026x^53+3739x^54+4510x^55+4669x^56+4482x^57+3806x^58+2492x^59+1412x^60+926x^61+379x^62+206x^63+50x^64+30x^65+19x^66+8x^67+7x^68+2x^72

The gray image is a code over GF(2) with n=448, k=15 and d=200.
This code was found by Heurico 1.16 in 8.51 seconds.