The generator matrix

1 0 0 0 0 1 1 1 1 2 1 1 1
0 1 0 0 0 1 0 0 3 1 2 2 0
0 0 1 0 0 1 2 3 0 3 0 2 0
0 0 0 1 0 1 3 2 2 1 0 0 0
0 0 0 0 1 2 1 3 1 1 3 1 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+100x^9+134x^10+68x^11+42x^12+136x^13+214x^14+168x^15+51x^16+20x^17+34x^18+20x^19+6x^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 1.10 in 0 seconds.