The generator matrix

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

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+26x^4+128x^5+352x^6+1032x^7+365x^8+112x^9+24x^10+8x^11

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 3.81e-009 seconds.