The generator matrix

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

generates a code of length 28 over GR(16,4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+681x^72+420x^73+324x^74+732x^75+3528x^76+1356x^77+984x^78+1968x^79+6591x^80+2976x^81+1596x^82+4104x^83+11022x^84+4080x^85+1908x^86+4464x^87+10335x^88+3036x^89+1200x^90+1020x^91+2616x^92+420x^93+132x^94+24x^96+18x^100

The gray image is a code over GF(4) with n=112, k=8 and d=72.
This code was found by Heurico 1.16 in 6.49 seconds.