The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+24x^6+48x^7+71x^8+80x^9+64x^10+80x^11+71x^12+48x^13+24x^14+1x^20

The gray image is a code over GF(2) with n=20, k=9 and d=6.
This code was found by Heurico 1.16 in 0.00152 seconds.