The generator matrix
1 1 1 1 X X X
0 2 0 2 0 2 0
0 0 2 2 2 2 0
generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+6x^6+16x^7+7x^8+2x^10
The gray image is a code over GF(2) with n=28, k=5 and d=12.
This code was found by Heurico 1.16 in 0.000131 seconds.