The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^12+16x^13+6x^14+1x^16+2x^18

The gray image is a code over GF(2) with n=26, k=5 and d=12.
This code was found by Heurico 1.16 in 0.000363 seconds.