The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+77x^8+296x^12+256x^14+331x^16+56x^20+7x^24

The gray image is a code over GF(2) with n=28, k=10 and d=8.
This code was found by Heurico 1.16 in 0.0112 seconds.