The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^4+32x^5+85x^6+704x^7+85x^8+32x^9+42x^10+1x^14

The gray image is a code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in 3.81e-009 seconds.