The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+307x^8+472x^10+1268x^12+1232x^14+571x^16+216x^18+28x^20+1x^24

The gray image is a code over GF(2) with n=26, k=12 and d=8.
This code was found by Heurico 1.10 in 21.2 seconds.