The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+45x^4+104x^6+242x^8+240x^10+242x^12+104x^14+45x^16+1x^20

The gray image is a code over GF(2) with n=20, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00187 seconds.