The generator matrix
1 1 1 1 0 0 2X
0 X 0 X X X X
0 0 X X 2X+2 0 2
0 0 0 2X 0 2X 2X
0 0 0 0 2X 2X 2X
generates a code of length 7 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+122x^4+160x^5+773x^6+1984x^7+773x^8+160x^9+122x^10+1x^14
The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.