The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+94x^6+240x^8+348x^10+260x^12+70x^14+11x^16

The gray image is a code over GF(2) with n=20, k=10 and d=6.
This code was found by Heurico 1.10 in 0 seconds.