The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+84x^6+68x^7+321x^8+300x^9+685x^10+996x^11+959x^12+1388x^13+957x^14+940x^15+682x^16+356x^17+319x^18+44x^19+85x^20+4x^21+3x^22

The gray image is a code over GF(2) with n=26, k=13 and d=6.
This code was found by Heurico 1.10 in 0.0974 seconds.