The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+22x^57+3x^58+3x^60+2x^61+1x^62

The gray image is a code over GF(2) with n=224, k=5 and d=114.
This code was found by Heurico 1.16 in 0.281 seconds.