The generator matrix

 1  0  0  0  1  1  1  1
 0  1  0  0  0  1  2  0
 0  0  1  0  1  1  3  0
 0  0  0  1  1  2  2  0
 0  0  0  0  2  0  2  0

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

Homogenous weight enumerator: w(x)=1x^0+38x^4+34x^5+57x^6+88x^7+61x^8+108x^9+66x^10+24x^11+28x^12+2x^13+5x^14

The gray image is a code over GF(2) with n=16, k=9 and d=4.
This code was found by Heurico 1.16 in 0.000742 seconds.