The generator matrix

 1  0  1  1  1  1  1  1
 0  1  1  0  0  0  0  0
 0  0  2  0  0  0  0  0
 0  0  0  2  0  0  0  0
 0  0  0  0  2  0  0  0
 0  0  0  0  0  2  0  0
 0  0  0  0  0  0  2  0
 0  0  0  0  0  0  0  2

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

Homogenous weight enumerator: w(x)=1x^0+12x^2+52x^4+116x^6+256x^7+150x^8+256x^9+116x^10+52x^12+12x^14+1x^16

The gray image is a code over GF(2) with n=16, k=10 and d=2.
This code was found by Heurico 1.16 in 0.00159 seconds.