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

generates a code of length 30 over GR(16,4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+138x^76+48x^79+609x^80+48x^81+288x^83+1329x^84+432x^85+768x^87+2868x^88+1296x^89+1248x^91+3084x^92+1296x^93+720x^95+1824x^96+249x^100+78x^104+48x^108+12x^112

The gray image is a code over GF(4) with n=120, k=7 and d=76.
This code was found by Heurico 1.16 in 0.556 seconds.