The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+28x^9+71x^10+108x^11+109x^12+120x^13+147x^14+120x^15+130x^16+108x^17+37x^18+28x^19+15x^20+1x^22+1x^24

The gray image is a code over GF(2) with n=28, k=10 and d=9.
This code was found by Heurico 1.16 in 0.108 seconds.