The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  2 2a+2 2a+2  0  2 2a+2  0  2 2a+2 2a 2a 2a 2a  0  0  2  2  0  2 2a 2a
 0  0  2 2a+2 2a+2  2 2a 2a  0 2a+2  2 2a  0  2 2a 2a+2  0  2 2a+2 2a 2a  2  0  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+18x^68+222x^72+6x^76+6x^80+3x^96

The gray image is a code over GF(4) with n=96, k=4 and d=68.
This code was found by Heurico 1.16 in 0 seconds.