The generator matrix

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

generates a code of length 8 over GR(16,4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+21x^12+105x^16+210x^20+3366x^24+297x^28+96x^32

The gray image is a code over GF(4) with n=32, k=6 and d=12.
This code was found by Heurico 1.16 in 0.00436 seconds.