The generator matrix

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

generates a code of length 15 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+161x^10+324x^12+524x^14+565x^16+326x^18+132x^20+12x^22+2x^24+1x^26

The gray image is a code over GF(2) with n=30, k=11 and d=10.
This code was found by Heurico 1.16 in 15.3 seconds.