The generator matrix

 1  0  0  0  1  1  1  0  1  1  2  1  1
 0  1  0  0  0  1  1  1  0  2  0  2  2
 0  0  1  0  1  1  0  1  0  1  1  0  0
 0  0  0  1  1  0  1  1  1  0  1  1  1
 0  0  0  0  2  0  0  0  0  0  2  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
 0  0  0  0  0  0  0  2  0  2  2  2  2
 0  0  0  0  0  0  0  0  2  2  0  0  2

generates a code of length 13 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+64x^6+375x^8+1288x^10+2368x^12+2360x^14+1303x^16+376x^18+48x^20+8x^22+1x^24

The gray image is a code over GF(2) with n=26, k=13 and d=6.
This code was found by Heurico 1.16 in 0.25 seconds.