The generator matrix
1 1 1 1 1 1 1
0 2 0 0 2X 2 0
0 0 2 0 2 2 2X
0 0 0 2 2X+2 2X 0
generates a code of length 7 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+26x^4+32x^5+37x^6+832x^7+37x^8+32x^9+26x^10+1x^14
The gray image is a code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.