The generator matrix

1 0 0 0 0 0 0 1
0 1 0 0 0 0 0 1
0 0 1 0 0 0 0 1
0 0 0 1 0 0 0 1
0 0 0 0 1 0 0 1
0 0 0 0 0 1 0 1
0 0 0 0 0 0 1 1

generates a code of length 8 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+56x^2+924x^4+3976x^6+6470x^8+3976x^10+924x^12+56x^14+1x^16

The gray image is a code over GF(2) with n=16, k=14 and d=2.
This code was found by Heurico 1.10 in 0.000942 seconds.