The generator matrix

 1  0  0  0  0  1  1  1  2  0  1  2  2  1
 0  1  0  0  0  0  0  0  1  2  1  1  2  2
 0  0  1  0  0  0  1  1  1  1  1  2  1  3
 0  0  0  1  0  1  1  0  1  3  1  1  0  1
 0  0  0  0  1  1  0  1  1  1  1  0  0  2
 0  0  0  0  0  2  0  0  0  0  2  2  2  0
 0  0  0  0  0  0  2  0  0  2  2  0  0  2
 0  0  0  0  0  0  0  2  0  0  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+262x^8+740x^10+1824x^12+2500x^14+1901x^16+716x^18+232x^20+12x^22+4x^24

The gray image is a code over GF(2) with n=28, k=13 and d=8.
This code was found by Heurico 1.16 in 0.6 seconds.