The generator matrix

 1  0  1  1  1  0  1
 0  1 X+1 X+2  3  1  0
 0  0 2X  0  0 2X  0
 0  0  0 2X  0 2X  0
 0  0  0  0 2X 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+18x^4+160x^5+301x^6+1088x^7+301x^8+160x^9+18x^10+1x^14

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 -3.24e-008 seconds.