The generator matrix
1 1 1 1 1 1 1 2 1 1
0 2 0 0 0 0 0 2 2 0
0 0 2 0 0 0 2 2 2 0
0 0 0 2 0 0 2 0 0 2
0 0 0 0 2 0 2 0 2 2
0 0 0 0 0 2 2 2 0 0
generates a code of length 10 over Z4 who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+9x^6+16x^8+32x^9+15x^10+32x^11+12x^12+7x^14+3x^16+1x^18
The gray image is a code over GF(2) with n=20, k=7 and d=6.
This code was found by Heurico 1.16 in 0.000398 seconds.