The generator matrix

 1  0  1  1  1  1  1  1  1  1  1
 0  1  1  a 3a+3  0 2a+3  a a+1  0 2a+3
 0  0 2a+2  0  0  0  2  0  2 2a 2a+2
 0  0  0  2  0  0 2a+2  2  2 2a  2
 0  0  0  0 2a+2  0  2 2a+2  0 2a 2a
 0  0  0  0  0  2 2a+2 2a+2  2 2a+2 2a+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+780x^24+1536x^27+3951x^28+3072x^30+9216x^31+11523x^32+9216x^34+13824x^35+11523x^36+528x^40+201x^44

The gray image is a code over GF(4) with n=44, k=8 and d=20.
This code was found by Heurico 1.16 in 1.46 seconds.