The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+13x^10+24x^11+8x^12+2x^14+8x^15+7x^16+1x^18

The gray image is a code over GF(2) with n=24, k=6 and d=10.
This code was found by Heurico 1.16 in 0.000364 seconds.