The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+42x^10+66x^11+44x^12+82x^13+70x^14+44x^15+67x^16+44x^17+30x^18+18x^19+2x^21+2x^22

The gray image is a code over GF(2) with n=28, k=9 and d=10.
This code was found by Heurico 1.10 in 0.015 seconds.