The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+47x^8+44x^10+22x^12+12x^14+2x^16

The gray image is a code over GF(2) with n=20, k=7 and d=8.
This code was found by Heurico 1.16 in 0.00122 seconds.