The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^6+388x^8+934x^10+1682x^12+2030x^14+1651x^16+978x^18+366x^20+74x^22+8x^24

The gray image is a code over GF(2) with n=28, k=13 and d=6.
This code was found by Heurico 1.10 in 0.182 seconds.