The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+38x^8+64x^9+24x^10+24x^12+64x^13+40x^14+1x^16

The gray image is a code over GF(2) with n=22, k=8 and d=8.
This code was found by Heurico 1.16 in 0.00147 seconds.