The generator matrix

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

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+120x^28+7x^32

The gray image is a code over GF(2) with n=224, k=7 and d=112.
This code was found by Heurico 1.16 in 0.016 seconds.