The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+68x^2+629x^4+96x^5+2048x^6+1760x^7+3466x^8+6336x^9+3960x^10+6336x^11+3466x^12+1760x^13+2048x^14+96x^15+629x^16+68x^18+1x^20

The gray image is a code over GF(2) with n=20, k=15 and d=2.
This code was found by Heurico 1.16 in 0.784 seconds.