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.