The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+119x^8+328x^10+576x^12+560x^14+375x^16+72x^18+16x^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 0.0546 seconds.