The generator matrix

 1  1  1  1  X  X  X
 0  X  0 X+2 3X+2 3X+2 3X+2
 0  0  2 2X+2  0  0 2X
 0  0  0 2X  0 2X 2X
 0  0  0  0 2X 2X  0

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+75x^4+64x^5+304x^6+1152x^7+319x^8+64x^9+64x^10+5x^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 -1.01e-007 seconds.