The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  X  X X^2 X^2 X^2  X  X  X  1  1 X^2
 0  2  0  2  0  0  2  2  0  0  2  0  2  2  2  0  0  2  0  2  0  2  2  0  0  2  2  0
 0  0  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  0  2  0  0

generates a code of length 28 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+56x^28+7x^32

The gray image is a code over GF(2) with n=224, k=6 and d=112.
This code was found by Heurico 1.16 in -3.24e-008 seconds.