The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+130x^3+1002x^4+5528x^5+24085x^6+69580x^7+24085x^8+5528x^9+1002x^10+130x^11+1x^14

The gray image is a code over GF(2) with n=56, k=17 and d=12.
This code was found by Heurico 1.16 in 3.34 seconds.