The generator matrix
1 0 1 1 1 1 1
0 1 1 0 X+2 X 0
0 0 X X+2 0 X 2
0 0 0 2 2 2 0
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+15x^4+36x^5+114x^6+184x^7+109x^8+36x^9+14x^10+3x^12
The gray image is a code over GF(2) with n=28, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000455 seconds.