The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+119x^4+8x^5+715x^6+288x^7+2504x^8+2464x^9+5428x^10+7904x^11+7582x^12+11440x^13+7714x^14+7904x^15+5329x^16+2464x^17+2548x^18+288x^19+715x^20+8x^21+107x^22+6x^24

The gray image is a code over GF(2) with n=26, k=16 and d=4.
This code was found by Heurico 1.10 in 0.557 seconds.