The generator matrix

 1  0  0  0  1  1  1  1  X  1  0  1  2  X  1  1  1  1  2  1  2  1  1 X+2  1  X  1  2  0  1  1  1  0 X+2  1  X  1 X+2  1  1  1  1  0  1  1 X+2  X  1  1  1  0  1  1  0  2  1
 0  1  0  0  0  1  2  3  1  0  1  1  1  2  3  X  3  1  X  1  1  X X+2  1  3  X  2  X  1  0 X+1  0  X  1 X+1  0  2  1 X+3 X+2  0  1  X  1  3  0  2 X+3 X+3 X+2  1  3 X+2  0  X  1
 0  0  1  0  1  2  0  3  1 X+1  X X+3  1  1  0 X+2 X+3 X+2 X+2 X+1  2  3  2  X X+2  1  1  1 X+3  X X+1 X+3  1 X+2  0  2 X+1 X+3  X  1  0  3  0  X  2  1  1  2 X+2 X+2  3  2  0 X+2  2  0
 0  0  0  1  2  0  1  3 X+3  3 X+3  X  X  3 X+3 X+2  0  2  1  1 X+1 X+1  2  2  1  1 X+2  2 X+2  1 X+3 X+1  1  X  X  1  2  3 X+1  X X+2  3  1 X+3  3 X+1  0  1  1 X+1  2  X  1  1  1  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+68x^50+280x^51+421x^52+444x^53+424x^54+428x^55+385x^56+286x^57+333x^58+292x^59+183x^60+164x^61+143x^62+118x^63+82x^64+30x^65+7x^66+4x^69+1x^70+2x^71

The gray image is a code over GF(2) with n=224, k=12 and d=100.
This code was found by Heurico 1.11 in 0.279 seconds.