The generator matrix

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

generates a code of length 30 over GR(16,4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+183x^72+309x^76+432x^80+192x^81+507x^84+1728x^85+549x^88+5184x^89+591x^92+5184x^93+651x^96+477x^100+237x^104+132x^108+24x^112+3x^120

The gray image is a code over GF(4) with n=120, k=7 and d=72.
This code was found by Heurico 1.16 in 1.09 seconds.