The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^10+44x^12+24x^14+3x^16+8x^18

The gray image is a code over GF(2) with n=24, k=7 and d=10.
This code was found by Heurico 1.16 in 0.0057 seconds.