The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+31x^6+112x^7+197x^8+348x^9+606x^10+928x^11+1222x^12+1324x^13+1196x^14+912x^15+609x^16+372x^17+210x^18+96x^19+18x^20+4x^21+5x^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 0.238 seconds.