The generator matrix

 1  1  1  1  1  1  1
 0 2X+2  0  0 2X 2X+2  0
 0  0 2X+2  0 2X+2 2X+2 2X
 0  0  0 2X+2  2 2X  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+26x^4+32x^5+37x^6+832x^7+37x^8+32x^9+26x^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 -3.24e-008 seconds.