The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^5+96x^6+240x^7+488x^8+792x^9+1267x^10+1890x^11+2249x^12+2324x^13+2227x^14+1806x^15+1282x^16+864x^17+497x^18+222x^19+75x^20+24x^21+9x^22+2x^23+1x^24

The gray image is a code over GF(2) with n=26, k=14 and d=5.
This code was found by Heurico 1.10 in 0.134 seconds.