The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+54x^5+166x^6+404x^7+1032x^8+2036x^9+3357x^10+5264x^11+7320x^12+8620x^13+9092x^14+8648x^15+7097x^16+5240x^17+3594x^18+2032x^19+928x^20+430x^21+174x^22+36x^23+6x^24+4x^25+1x^26

The gray image is a code over GF(2) with n=28, k=16 and d=5.
This code was found by Heurico 1.10 in 1.07 seconds.