The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+28x^7+135x^8+214x^9+431x^10+592x^11+869x^12+1234x^13+1191x^14+1164x^15+940x^16+634x^17+405x^18+200x^19+103x^20+30x^21+21x^22

The gray image is a code over GF(2) with n=28, k=13 and d=7.
This code was found by Heurico 1.10 in 0.104 seconds.