The generator matrix

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

generates a code of length 20 over GR(16,4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+180x^44+315x^48+426x^52+639x^56+13068x^60+798x^64+570x^68+321x^72+60x^76+6x^80

The gray image is a code over GF(4) with n=80, k=7 and d=44.
This code was found by Heurico 1.16 in 0.574 seconds.