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

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

Homogenous weight enumerator: w(x)=1x^0+114x^4+24x^5+552x^6+322x^7+1604x^8+1558x^9+2492x^10+3794x^11+3424x^12+4998x^13+3444x^14+3766x^15+2477x^16+1586x^17+1604x^18+310x^19+566x^20+26x^21+100x^22+6x^24

The gray image is a code over GF(2) with n=26, k=15 and d=4.
This code was found by Heurico 1.10 in 0.188 seconds.