The generator matrix

 1  0  1  1  1  1  1  1  1  0  1
 0  1  1  a 3a+3  0 2a+3  a a+1  1  a
 0  0 2a+2  0  0  2  0 2a 2a  2 2a
 0  0  0  2  0 2a+2 2a 2a+2  2  2 2a+2
 0  0  0  0 2a+2  2  2 2a+2 2a+2  2  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+213x^24+768x^27+597x^28+4608x^31+1461x^32+6912x^35+1626x^36+165x^40+33x^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 0.105 seconds.