The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+121x^8+336x^10+522x^12+656x^14+301x^16+96x^18+14x^20+1x^24

The gray image is a code over GF(2) with n=26, k=11 and d=8.
This code was found by Heurico 1.16 in 0.0358 seconds.