The generator matrix

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

generates a code of length 8 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+140x^4+448x^6+870x^8+448x^10+140x^12+1x^16

The gray image is a code over GF(2) with n=16, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00681 seconds.