The generator matrix
1 0 1 1 1 1 1
0 1 X+1 0 0 0 0
0 0 2 0 0 0 0
0 0 0 2 0 0 0
0 0 0 0 2 0 0
0 0 0 0 0 2 0
0 0 0 0 0 0 2
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+19x^2+81x^4+539x^6+768x^7+539x^8+81x^10+19x^12+1x^14
The gray image is a code over GF(2) with n=28, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00128 seconds.