The generator matrix

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

generates a code of length 11 over GR(16,4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+165x^20+396x^24+495x^28+1155x^32+12288x^33+1155x^36+528x^40+201x^44

The gray image is a code over GF(4) with n=44, k=7 and d=20.
This code was found by Heurico 1.16 in 0.158 seconds.