The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+149x^8+378x^10+946x^12+1138x^14+957x^16+398x^18+118x^20+6x^22+5x^24

The gray image is a code over GF(2) with n=28, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0942 seconds.