The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+172x^2+1354x^3+5510x^4+6840x^5+44493x^6+145404x^7+44493x^8+6840x^9+5510x^10+1354x^11+172x^12+1x^14

The gray image is a code over GF(2) with n=56, k=18 and d=8.
This code was found by Heurico 1.16 in 8.03 seconds.