The generator matrix

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

generates a code of length 30 over GR(16,4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+348x^80+192x^84+1392x^88+1728x^92+285x^96+120x^104+30x^112

The gray image is a code over GF(4) with n=120, k=6 and d=80.
This code was found by Heurico 1.16 in 90 seconds.