The generator matrix
1 0 1 1 1 1 1
0 1 1 0 0 0 0
0 0 X 0 0 2 0
0 0 0 X 0 2 0
0 0 0 0 X 2 0
generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+36x^2+42x^3+142x^4+216x^5+845x^6+1532x^7+845x^8+216x^9+142x^10+42x^11+36x^12+1x^14
The gray image is a code over GF(2) with n=28, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00431 seconds.