The generator matrix

 1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  2  0 2a  2  2 2a+2
 0  0  2  0  0 2a+2  2  0 2a+2 2a  2
 0  0  0  2  0  2 2a+2 2a+2  0  2  2
 0  0  0  0  2 2a+2 2a  2  2  0  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+165x^24+165x^28+165x^32+3072x^33+330x^36+165x^40+33x^44

The gray image is a code over GF(4) with n=44, k=6 and d=24.
This code was found by Heurico 1.16 in 0.0138 seconds.