The generator matrix
1 0 1 1 1 X 1
0 1 1 0 0 0 0
0 0 X 0 0 X 0
0 0 0 X 0 X 0
0 0 0 0 X X 0
0 0 0 0 0 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+53x^2+68x^3+347x^4+752x^5+1647x^6+2456x^7+1647x^8+752x^9+347x^10+68x^11+53x^12+1x^14
The gray image is a code over GF(2) with n=28, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0202 seconds.