The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^9+77x^10+86x^11+98x^12+136x^13+152x^14+140x^15+119x^16+82x^17+58x^18+30x^19+6x^20+4x^21+1x^26

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 0.0121 seconds.