The generator matrix

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

generates a code of length 11 over GR(16,4) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+84x^27+300x^28+288x^29+48x^30+504x^31+600x^32+384x^33+144x^34+756x^35+693x^36+288x^37+3x^40+3x^44

The gray image is a code over GF(4) with n=44, k=6 and d=27.
This code was found by Heurico 1.16 in 0.016 seconds.