The generator matrix

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

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+96x^50+302x^51+335x^52+464x^53+346x^54+518x^55+366x^56+376x^57+257x^58+314x^59+197x^60+176x^61+124x^62+98x^63+43x^64+40x^65+25x^66+16x^67+2x^68

The gray image is a code over GF(2) with n=224, k=12 and d=100.
This code was found by Heurico 1.16 in 0.552 seconds.