The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+46x^12+15x^16+2x^20

The gray image is a code over GF(2) with n=26, k=6 and d=12.
This code was found by Heurico 1.16 in 0.00198 seconds.