The generator matrix

 1  0  0  1  1  1  2  1  2  2  1  1 X+2  1  1  X  1  2  1  X  1  0  X  1  1  1  0  0  1  1 X+2  1  2  1  0  1  1 X+2  1  0  X  X  0  0  1  1  1  1  1 X+2  X  1  1  1  1  1
 0  1  0  0  1  3  1  2  1  1 X+3 X+2  0 X+1 X+2  1  2  X X+3  1 X+3  0  1 X+1  1  X  1  1  2 X+2  1 X+1  1 X+1 X+2  X  X  1 X+2  1 X+2  1  1  1 X+3  1 X+3 X+1 X+2  1  1 X+2  3  3 X+1 X+1
 0  0  1  1  1  0  1  1  X X+3  1  2  1  0  3 X+2  X  1 X+2 X+3 X+1  1  0  X  1 X+2 X+2  1 X+3  2  X  0 X+1  1  1 X+1 X+2  3 X+3  1  1  0 X+1  2  1 X+3  3  0  X X+1 X+3 X+2  3  1  2  X
 0  0  0  X  0  0  2  0  0  2  2  0  0  2  2  0  2  0  2  X X+2 X+2 X+2  X X+2 X+2 X+2  X X+2 X+2  X  X  2 X+2 X+2  X X+2  X  2  X  X  2  0 X+2  0  X  2  2  X  2 X+2  2 X+2  0  X  X
 0  0  0  0  2  2  2  0  2  0  0  2  2  0  2  0  0  0  2  2  0  2  0  0  2  0  2  0  2  2  0  2  2  0  0  2  2  2  2  2  0  2  0  2  2  0  2  2  2  0  2  0  0  0  2  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+176x^50+160x^51+509x^52+164x^53+684x^54+220x^55+597x^56+176x^57+440x^58+160x^59+346x^60+100x^61+208x^62+28x^63+73x^64+8x^65+24x^66+8x^67+9x^68+4x^70+1x^72

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 0.689 seconds.