The generator matrix

 1  0  1  1  1  1  1  1  1  2  1
 0  1 2a+3  a a+1  2 2a+1 a+2 a+3  1 2a

generates a code of length 11 over GR(16,4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+96x^31+39x^32+96x^35+24x^36

The gray image is a code over GF(4) with n=44, k=4 and d=31.
This code was found by Heurico 1.16 in -3.62e-008 seconds.