The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+93x^4+576x^5+408x^6+1920x^7+443x^8+576x^9+72x^10+7x^12

The gray image is a code over GF(2) with n=28, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00725 seconds.