The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+18x^10+28x^12+13x^14+3x^16+1x^22

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 0.00047 seconds.