The generator matrix

 1  1  1  1  1  1  1  1  1  1
 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  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  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

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

Homogenous weight enumerator: w(x)=1x^0+10x^2+45x^4+120x^6+210x^8+1276x^10+210x^12+120x^14+45x^16+10x^18+1x^20

The gray image is a code over GF(2) with n=20, k=11 and d=2.
This code was found by Heurico 1.16 in 0.00534 seconds.