The generator matrix

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

generates a code of length 24 over GR(16,4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+147x^68+192x^69+144x^70+159x^72+96x^73+129x^76+96x^77+48x^78+9x^80+3x^96

The gray image is a code over GF(4) with n=96, k=5 and d=68.
This code was found by Heurico 1.16 in 3.24e-008 seconds.