The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+28x^26+198x^28+28x^30+1x^56

The gray image is a code over GF(2) with n=112, k=8 and d=52.
This code was found by Heurico 1.16 in 0.019 seconds.