The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+36x^5+148x^6+312x^7+737x^8+1532x^9+2502x^10+3776x^11+4826x^12+5116x^13+4766x^14+3672x^15+2501x^16+1604x^17+770x^18+304x^19+126x^20+32x^21+6x^22+1x^24

The gray image is a code over GF(2) with n=26, k=15 and d=5.
This code was found by Heurico 1.16 in 2.85 seconds.