The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+102x^50+80x^51+218x^52+144x^53+206x^54+160x^55+238x^56+160x^57+242x^58+144x^59+164x^60+80x^61+80x^62+15x^64+6x^66+2x^70+2x^72+2x^74+2x^84

The gray image is a code over GF(2) with n=224, k=11 and d=100.
This code was found by Heurico 1.16 in 2.83 seconds.