The generator matrix

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

generates a code of length 29 over GR(16,4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+42x^72+108x^74+108x^75+225x^76+204x^78+372x^79+762x^80+504x^82+1368x^83+1782x^84+792x^86+2184x^87+2499x^88+924x^90+1788x^91+1581x^92+540x^94+324x^95+123x^96+84x^100+45x^104+24x^108

The gray image is a code over GF(4) with n=116, k=7 and d=72.
This code was found by Heurico 1.16 in 0.522 seconds.