The generator matrix
1 0 0 0 0 1 1
0 1 0 0 0 X 0
0 0 1 0 0 X 0
0 0 0 1 0 X 0
0 0 0 0 1 X 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+92x^2+318x^3+1238x^4+2920x^5+6605x^6+10420x^7+6605x^8+2920x^9+1238x^10+318x^11+92x^12+1x^14
The gray image is a code over GF(2) with n=28, k=15 and d=4.
This code was found by Heurico 1.13 in 0.00534 seconds.