The generator matrix

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

generates a code of length 11 over GR(16,4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+15x^28+24x^32+192x^33+15x^36+3x^40+6x^44

The gray image is a code over GF(4) with n=44, k=4 and d=28.
This code was found by Heurico 1.16 in 3.24e-008 seconds.