The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  1  1
 0  1  0  0  0  1  1  1  2  2  3  2  0  1
 0  0  1  0  1  1  0  3  2  0  3  2  1  0
 0  0  0  1  1  2  3  1  2  3  3  0  1  1
 0  0  0  0  2  0  2  0  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+58x^10+151x^12+108x^14+126x^16+58x^18+9x^20+1x^24

The gray image is a code over GF(2) with n=28, k=9 and d=10.
This code was found by Heurico 1.16 in 0.0192 seconds.