The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+19x^28+4x^29+3x^30+4x^31+1x^34

The gray image is a code over GF(2) with n=112, k=5 and d=56.
This code was found by Heurico 1.16 in 0.00477 seconds.