The generator matrix

1 0 0 0 0 0 0 1 1 1 1 1 1
0 1 0 0 0 0 0 0 1 1 2 0 0
0 0 1 0 0 0 0 0 1 2 1 1 0
0 0 0 1 0 0 0 0 2 1 3 2 0
0 0 0 0 1 0 0 1 0 1 3 3 0
0 0 0 0 0 1 0 1 0 3 2 1 0
0 0 0 0 0 0 1 1 3 1 2 2 0
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+44x^5+130x^6+310x^7+762x^8+1506x^9+2536x^10+3782x^11+4784x^12+5114x^13+4724x^14+3762x^15+2541x^16+1494x^17+792x^18+338x^19+104x^20+34x^21+10x^22

The gray image is a code over GF(2) with n=26, k=15 and d=5.
This code was found by Heurico 1.10 in 0.497 seconds.