The generator matrix

 1  0  1  1  1  1  1  1  1  1  1
 0  1  1  a a+1  0 2a+3 a+1  2 2a+3 a+3
 0  0 2a+2 2a  2  2  0 2a+2 2a 2a 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+111x^28+96x^30+267x^32+288x^34+246x^36+12x^40+3x^44

The gray image is a code over GF(4) with n=44, k=5 and d=28.
This code was found by Heurico 1.16 in -3.62e-008 seconds.