The generator matrix
1 1 1 1 1 1 1
0 2 0 0 0 2 0
0 0 2 0 0 2 0
0 0 0 2 0 2 0
0 0 0 0 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+10x^4+5x^6+96x^7+5x^8+10x^10+1x^14
The gray image is a code over GF(2) with n=28, k=7 and d=8.
This code was found by Heurico 1.16 in 0.00013 seconds.