The generator matrix

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

generates a code of length 22 over GR(16,4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+264x^56+192x^60+1515x^64+1728x^68+264x^72+132x^80

The gray image is a code over GF(4) with n=88, k=6 and d=56.
This code was found by Heurico 1.16 in 47.3 seconds.