The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^8+104x^9+130x^10+56x^11+54x^12+144x^13+206x^14+176x^15+43x^16+8x^17+46x^18+24x^19+2x^20+2x^22

The gray image is a code over GF(2) with n=26, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00965 seconds.