The generator matrix

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

generates a code of length 29 over GR(16,4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+2280x^76+7614x^80+15504x^84+21432x^88+16200x^92+2505x^96

The gray image is a code over GF(4) with n=116, k=8 and d=76.
This code was found by Heurico 1.16 in 41.5 seconds.