The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+2x^10+8x^11+3x^12+1x^14+1x^18

The gray image is a code over GF(2) with n=22, k=4 and d=10.
This code was found by Heurico 1.16 in 0.000179 seconds.