The generator matrix

 1  0  0  0  0  1  1  1  1  1
 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  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+50x^2+445x^4+2040x^6+7490x^8+12716x^10+7490x^12+2040x^14+445x^16+50x^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 0.778 seconds.