The generator matrix

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

generates a code of length 11 over GR(16,4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+126x^24+144x^25+108x^26+192x^27+1035x^28+432x^29+732x^30+1152x^31+2991x^32+1776x^33+2052x^34+1728x^35+2958x^36+720x^37+180x^38+42x^40+15x^44

The gray image is a code over GF(4) with n=44, k=7 and d=24.
This code was found by Heurico 1.16 in 0.094 seconds.