The generator matrix

 1  1  1  1  X  X  X
 0  X  0 X+2 3X+2 X+2 2X
 0  0  2  0  0 2X 2X+2
 0  0  0  2  0 2X+2 2X
 0  0  0  0 2X  0 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+109x^4+160x^5+904x^6+1728x^7+939x^8+160x^9+88x^10+7x^12

The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in -1.01e-007 seconds.