The generator matrix

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

generates a code of length 21 over GR(16,4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+576x^57+564x^60+864x^61+159x^64+1152x^65+288x^68+480x^69+12x^76

The gray image is a code over GF(4) with n=84, k=6 and d=57.
This code was found by Heurico 1.16 in 128 seconds.