The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+200x^6+1546x^8+6264x^10+15076x^12+19480x^14+14761x^16+6536x^18+1492x^20+160x^22+20x^24

The gray image is a code over GF(2) with n=28, k=16 and d=6.
This code was found by Heurico 1.10 in 33 seconds.