The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+171x^56+180x^57+36x^58+528x^59+1137x^60+972x^61+180x^62+816x^63+1707x^64+1908x^65+300x^66+1584x^67+2142x^68+1956x^69+252x^70+912x^71+1191x^72+360x^73+33x^76+18x^80

The gray image is a code over GF(4) with n=88, k=7 and d=56.
This code was found by Heurico 1.16 in 0.281 seconds.