The generator matrix

 1  0  0  0  0  1  1  1  1  1  2  1  1  1  1
 0  1  0  0  0  0  0  0  3  1  1  2  1  1  2
 0  0  1  0  0  0  1  2  3  0  3  3  2  3  0
 0  0  0  1  0  0  1  3  2  3  2  1  2  0  1
 0  0  0  0  1  1  2  1  3  2  2  1  3  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  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+151x^10+360x^12+481x^14+575x^16+345x^18+116x^20+15x^22+4x^24

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 26.5 seconds.