The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+77x^4+296x^6+1280x^7+331x^8+56x^10+7x^12

The gray image is a code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.