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

generates a code of length 30 over GR(16,4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+135x^84+366x^88+468x^92+21x^96+6x^100+6x^104+12x^108+6x^112+3x^116

The gray image is a code over GF(4) with n=120, k=5 and d=84.
This code was found by Heurico 1.16 in 0.75 seconds.