The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+106x^6+537x^8+1512x^10+3732x^12+4676x^14+3543x^16+1688x^18+492x^20+82x^22+15x^24

The gray image is a code over GF(2) with n=28, k=14 and d=6.
This code was found by Heurico 1.10 in 0.237 seconds.