The generator matrix
1 0 1 1 1 0 1
0 1 X+1 X+2 1 1 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+18x^4+64x^5+109x^6+128x^7+109x^8+64x^9+18x^10+1x^14
The gray image is a code over GF(2) with n=28, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000356 seconds.