The generator matrix

 1  0  1  1  1  0  1  1
 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  0  0

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

Homogenous weight enumerator: w(x)=1x^0+18x^4+24x^6+42x^8+24x^10+18x^12+1x^16

The gray image is a code over GF(2) with n=16, k=7 and d=4.
This code was found by Heurico 1.16 in 0.000192 seconds.