The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+78x^72+60x^73+132x^74+336x^75+813x^76+1068x^77+576x^78+1464x^79+2034x^80+2640x^81+1560x^82+2784x^83+4461x^84+6216x^85+2640x^86+5232x^87+6753x^88+7500x^89+3204x^90+4368x^91+4404x^92+3852x^93+1104x^94+1176x^95+789x^96+168x^97+57x^100+51x^104+9x^108+6x^112

The gray image is a code over GF(4) with n=116, k=8 and d=72.
This code was found by Heurico 1.16 in 6.94 seconds.