The generator matrix

 1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  2  0  2
 0  0  2  0  0  0 2a+2  2 2a+2
 0  0  0  2  0  0  2 2a+2  0
 0  0  0  0  2  0 2a+2  2  0
 0  0  0  0  0  2 2a  2  2

generates a code of length 9 over GR(16,4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+36x^12+174x^16+480x^20+912x^24+12288x^27+1284x^28+897x^32+312x^36

The gray image is a code over GF(4) with n=36, k=7 and d=12.
This code was found by Heurico 1.16 in 0.0638 seconds.