The generator matrix

 1  1  1  1  X  X  1
 0 2X+2  0  2 2X 2X  0
 0  0 2X+2  2  2  2  0
 0  0  0 2X  0 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+16x^4+34x^5+16x^6+382x^7+13x^8+30x^9+16x^10+2x^11+2x^12

The gray image is a code over GF(2) with n=56, k=9 and d=16.
This code was found by Heurico 1.16 in -1.01e-007 seconds.