The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+188x^6+707x^8+1920x^10+3360x^12+4088x^14+3199x^16+2080x^18+656x^20+172x^22+13x^24

The gray image is a code over GF(2) with n=28, k=14 and d=6.
This code was found by Heurico 1.16 in 1.77 seconds.