The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  1  1  1  1  1  1  0  2 X+2  X  1  1  1  1
 0  1 X+1 X+2  3  1  2 X+3  1  X  1  1  0 X+1 X+2  3  2  X X+3  1  1  1  1  1  0  2 X+2  X

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+60x^28+1x^32+2x^40

The gray image is a code over GF(2) with n=112, k=6 and d=56.
This code was found by Heurico 1.16 in 0.00335 seconds.