The generator matrix

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

generates a code of length 29 over GR(16,4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+174x^80+288x^81+192x^82+792x^84+672x^85+336x^86+240x^88+96x^89+96x^90+456x^92+480x^93+144x^94+129x^96

The gray image is a code over GF(4) with n=116, k=6 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.