The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+17x^6+64x^8+95x^10+60x^12+15x^14+3x^16+1x^18

The gray image is a code over GF(2) with n=20, k=8 and d=6.
This code was found by Heurico 1.16 in 0.000784 seconds.