The generator matrix

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

generates a code of length 9 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+22x^4+62x^5+67x^6+108x^7+167x^8+164x^9+166x^10+128x^11+64x^12+46x^13+23x^14+4x^15+2x^16

The gray image is a code over GF(2) with n=18, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00335 seconds.