The generator matrix

 1  1  X  1  1  1  1
 0 2X+2 2X+2  0  0 2X  0
 0  0 2X  0 2X 2X  0
 0  0  0 2X 2X  0  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+8x^4+40x^6+160x^7+37x^8+8x^10+2x^12

The gray image is a code over GF(2) with n=56, k=8 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.