The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  2
 0  2  0  0  0  0  0  0  0  0  0  2  0  2
 0  0  2  0  0  0  0  0  0  0  0  2  2  2
 0  0  0  2  0  0  0  0  0  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  2  0  2  2
 0  0  0  0  0  0  0  2  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  2
 0  0  0  0  0  0  0  0  0  2  2  2  2  2

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

Homogenous weight enumerator: w(x)=1x^0+28x^6+77x^8+112x^10+424x^12+744x^14+459x^16+112x^18+56x^20+28x^22+7x^24

The gray image is a code over GF(2) with n=28, k=11 and d=6.
This code was found by Heurico 1.16 in 0.0202 seconds.