The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^8+236x^10+416x^12+620x^14+505x^16+164x^18+56x^20+4x^22+2x^24

The gray image is a code over GF(2) with n=28, k=11 and d=8.
This code was found by Heurico 1.16 in 0.0334 seconds.